## Prof Peter Ashwin

#### Professor

**(Streatham) 5225**

**01392 725225**

## Overview

I am a Professor of Mathematics specializing in dynamical systems theory and computational modelling. I have been at Exeter since 2000, having previously held teaching and research positions at Surrey, Warwick, Nice (France) and Marburg (Germany). I am currently Adjunct Professor at the School of Mathematical Sciences at University College Cork..

**Research Interests**

My main interests are in nonlinear dynamical systems and applications: bifurcation theory and dynamical systems, especially synchronization problems, symmetric chaotic dynamics and spatially extended systems and nonautonomous systems. Applications of dynamical systems that I have been studying include climate (bifurcations, tipping points), fluids (bifurcations and mixing), laser systems (synchronization), neural systems (perceptual rivalry, intermittent models), materials and electronic systems (digital signal processing), biophysical modelling (cell biology).

Particular themes running through my work include symmetries and intermittent behaviour, and the structure of attractors, in particular, riddled basins of attraction and associated phenomena. I also have interests in random dynamics/stochastically forced systems and in low dimensional dynamics/ergodic theory.

Current research projects include the mathematical modelling of paleoclimate transitions, molecular networks, phase change materials in data storage media, using heteroclinic networks to model functional dynamics in neural and other biomedical systems and tipping points in nonautonomous systems with applications in climate and finance; for more detail see my publications.

In 2012 I was a co-founder of the "Maths for Climate" network "CliMathNet" with EPSRC funding. This continues as an international network of researchers interested in developing and applying cuttiing-edge mathematics and statistics to the Climate system. During 2015-2018 I led the project "ReCoVER" with Prof Tim Lenton (Exeter). I was Exeter coordinator of the EU Marie Curie ITN programme "CRITICS" looking at mathematics and applications of critical transitions (2015-2019). I was Co-I for a Leverhulme-funded project on ER-organelle interaction (PI: Imogen Sparkes) since 2015. I was Co-I for the EPSRC-funded "Centre for Predictive Modelling in Healthcare" (2016-2020), and the Exeter coordinator of the EU funded "TIPES: Tipping points in the Earth System" that launched in 2019. I am currently PI of the EPSRC funded project "Applied Nonlinear Nonautonomous Systems: Theory, Methods and Applications" 2020-2023 and am the Exeter PI for the EU Marie Curie ITN programme "CriticalEarth" running 2021-2025.

I am happy to supervise MMath, MSc or PhD projects in the areas of my research interests, or related areas of mathematics. Any available positions are advertised on the Centre for Systems Dynamics and Control blog.

**Teaching Interests**

I am currently teaching on:

- MTH3019 Mathematics; History and Culture
- MAGIC020 Dynamical Systems

I am also Director of the MAGIC mathematics PhD taught course centre, a consortium of UK universities.

**Other Relevant Information**

Since 2022 I am Director of Research and Impact within the Department of Mathematics and Statistics at Exeter.

I am Associate Editor for the journals Chaos: An interdisciplinary journal of nonlinear science, Dynamical Systems; an International Journal and Mathematical Neuroscience and Applications and a member of the EPSRC peer review college. I have been an editor for Journal of Mathematical Neuroscience and Frontiers in Applied Mathematics and Statistics. I served as Head of Mathematics and Computer Science at Exeter for the period 2010-14. I was secretary for the European Dynamics Days 2001-2008 and have contributed to activites of the SIAM activity groups on Dynamical Systems and Mathematics of Planet Earth. For 2021-24 I am serving on the Council of the London Mathematical Society. I was appointed as a Fellow of the Society of Industrial and Applied Mathematics in the class of 2024.

**Qualifications**

MA (Camb), CAS (Camb), PhD (Warwick), Senior Fellow of Higher Education Academy

**Booking a meeting**

Book a time for a personal tutorial

## Publications

_{Copyright Notice: Any articles made available for download are for personal use only. Any other use requires prior permission of the author and the copyright holder.}

| 2024 | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 | 2017 | 2016 | 2015 | 2014 | 2013 | 2012 | 2011 | 2010 | 2009 | 2008 | 2007 | 2006 | 2005 | 2004 | 2003 | 2002 | 2001 | 2000 | 1999 | 1998 | 1997 | 1996 | 1995 | 1994 | 1993 | 1992 | 1990 |

### 2024

- Ashwin P, Newman J, Römer R. (2024) Contrasting chaotic and stochastic forcing: tipping windows and attractor crises. [PDF]
- Chapman R, Ashwin P, Baker J, Wood RA. (2024) Quantifying risk of a noise-induced AMOC collapse from northern and tropical Atlantic Ocean variability. [PDF]
- Chapman R, Ashwin P, Wood R, Baker J. (2024) Quantifying risk of a noise-induced AMOC collapse from northern and tropical Atlantic Ocean variability, DOI:10.5194/egusphere-egu24-8729. [PDF]
- Roemer R, Ashwin P. (2024) Characterising Edge States: Measures on chaotic non-attracting invariant sets, DOI:10.5194/egusphere-egu24-18525. [PDF]
- Huang Y, Bathiany S, Ashwin P, Boers N. (2024) Anticipating rate-induced tipping by a deep learning framework, DOI:10.5194/egusphere-egu24-12187. [PDF]
- Sinet S, von der Heydt AS, Ashwin P, Dijkstra HA. (2024) AMOC Stability amid Tipping Ice Sheets from Conceptual to Intermediate Complexity Models, DOI:10.5194/egusphere-egu24-8397.
- Ashwin P, Fadera M, Postlethwaite C. (2024) Network attractors and nonlinear dynamics of neural computation,
*Current Opinion in Neurobiology*, volume 84, pages 102818-102818, article no. 102818, DOI:10.1016/j.conb.2023.102818. [PDF]

### 2023

- Clarke J. (2023) Tipping Points and Early Warning Signals in the Climate-Carbon System.
- Sinet S, Ashwin P, von der Heydt AS, Dijkstra HA. (2023) AMOC Stability Amid Tipping Ice Sheets: The Crucial Role of Rate and Noise, DOI:10.5194/egusphere-2023-2661. [PDF]
- Morr A, Boers N, Ashwin P. (2023) Internal noise interference in anticipation of tipping points of generic multi-dimensional dynamical systems. [PDF]
- Ashwin P, Ceni A. (2023) Transitions in echo index and dependence on input repetitions. [PDF]
- Wieczorek S, Xie C, Ashwin P. (2023) Rate-Induced Tipping: Thresholds, Edge States and Connecting Orbits,
*Nonlinearity*, DOI:10.1088/1361-6544/accb37. - Roemer R, Ashwin P. (2023) Fractal Dimension of nonattracting chaotic sets, DOI:10.5194/egusphere-egu23-16103. [PDF]
- Newman J, Ashwin P. (2023) Natural measures of asymptotically autonomous systems, DOI:10.5194/egusphere-egu23-17454. [PDF]
- Chapman R, Ashwin P, Wood R. (2023) Stochastic data adapted AMOC box models, DOI:10.5194/egusphere-egu23-406. [PDF]
- Newman J, Ashwin P. (2023) Physical measures of asymptotically autonomous dynamical systems,
*Stochastics and Dynamics*, volume 23, no. 3, DOI:10.1142/S021949372350020X. - Ashwin P, Lin C. (2023) Geometric dynamics of anchored filamentous networks,
*Communications in Nonlinear Science and Numerical Simulation*, DOI:10.1016/j.cnsns.2022.107012. - Hummel F, Ashwin P, Kuehn C. (2023) Reduction methods in climate dynamics—A brief review,
*Physica D: Nonlinear Phenomena*, volume 448, DOI:10.1016/j.physd.2023.133678. - Ashwin P, Creaser J, Tsaneva-Atanasova K. (2023) Quasipotentials for coupled escape problems and the gate-height bifurcation,
*Physical Review E*, volume 107, no. 1, article no. 014213, DOI:10.1103/physreve.107.014213. [PDF] - Bastiaansen R, Ashwin P, Heydt ASVD. (2023) Climate Response and Sensitivity: Timescales and Late Tipping Points,
*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, volume 479, DOI:10.1098/rspa.2022.0483.

### 2022

- Hakim L, Ashwin P. (2022) The impact of thinking fast and slow on teaching and learning strategies in mathematics,
*A Focus on Pedagogy: Teaching, Learning and Research in the Modern Academy*, Online, 20th - 22nd Apr 2022. [PDF] - Oljača L, Ashwin P, Rasmussen M. (2022) Correction to: Measure and Statistical Attractors for Nonautonomous Dynamical Systems (Journal of Dynamics and Differential Equations, (2022), 10.1007/s10884-022-10196-5),
*Journal of Dynamics and Differential Equations*, DOI:10.1007/s10884-022-10232-4. - Oljača L, Ashwin P, Rasmussen M. (2022) Measure and Statistical Attractors for Nonautonomous Dynamical Systems,
*Journal of Dynamics and Differential Equations*, DOI:10.1007/s10884-022-10196-5. [PDF] - Wedgwood KCA, Ashwin P. (2022) Morphogen-directed cell fate boundaries: slow passage through bifurcation and the role of folded saddles,
*Journal of Theoretical Biology*, volume 549, DOI:10.1016/j.jtbi.2022.111220. - Lux K, Ashwin P, Wood R, Kuehn C. (2022) Assessing the impact of parametric uncertainty on tipping points of the Atlantic meridional overturning circulation,
*Environmental Research Letters*, volume 17, no. 7, DOI:10.1088/1748-9326/ac7602. - Ashwin P, Bick C, Rodrigues A. (2022) From Symmetric Networks to Heteroclinic Dynamics and Chaos in Coupled Phase Oscillators with Higher-Order Interactions,
*Understanding Complex Systems*, 197-216, DOI:10.1007/978-3-030-91374-8_7. - Smug D, Ashwin J, Ashwin P, Sornette D. (2022) An adaptive dynamical model of default contagion,
*Quantitative Finance*, volume 22, no. 7, pages 1217-1227, DOI:10.1080/14697688.2022.2039755. [PDF] - Ashwin P, Postlethwaite C. (2022) Excitable networks for finite state computation with continuous time recurrent neural networks (vol 115, pg 519, 2021),
*BIOLOGICAL CYBERNETICS*, volume 116, no. 1, pages 117-117, DOI:10.1007/s00422-021-00911-8. [PDF]

### 2021

- Wieczorek S, Xie C, Ashwin P. (2021) Rate-Induced Tipping: Thresholds, Edge States and Connecting Orbits. [PDF]
- Ashwin P, Bick C, Poignard C. (2021) Dead zones and phase reduction of coupled oscillators,
*Chaos: An Interdisciplinary Journal of Nonlinear Science*, volume 31, no. 9, DOI:10.1063/5.0063423. [PDF] - Zerenner T, Goodfellow M, Ashwin P. (2021) Harmonic cross-correlation decomposition for multivariate time series,
*Physical Review E*, volume 103, no. 6, DOI:10.1103/PhysRevE.103.062213. - Ashwin P, Newman J. (2021) Physical invariant measures and tipping probabilities for chaotic attractors of asymptotically autonomous systems,
*European Physical Journal: Special Topics*, DOI:10.1140/epjs/s11734-021-00114-z. [PDF] - Newman J, Ashwin P. (2021) Re-thinking noise-induced tipping, DOI:10.5194/egusphere-egu21-5918. [PDF]
- Lin C, Ashwin P, Steinberg G. (2021) Modelling the motion of organelles in an elongated cell via the coordination of heterogeneous drift–diffusion and long-range transport,
*The European Physical Journal E*, volume 44, no. 2, article no. 10, DOI:10.1140/epje/s10189-020-00007-4. [PDF] - Ashwin P, Postlethwaite C. (2021) Excitable networks for finite state computation with continuous time recurrent neural networks,
*Biological Cybernetics*, volume 115, no. 5, pages 519-538, DOI:10.1007/s00422-021-00895-5. [PDF] - von der Heydt AS, Ashwin P, Camp CD, Crucifix M, Dijkstra HA, Ditlevsen P, Lenton TM. (2021) Quantification and interpretation of the climate variability record,
*Global and Planetary Change*, volume 197, DOI:10.1016/j.gloplacha.2020.103399. - Creaser J, Ashwin P, Postlethwaite C, Britz J. (2021) Noisy network attractor models for transitions between EEG microstates,
*The Journal of Mathematical Neuroscience*, volume 11, no. 1, article no. 1, DOI:10.1186/s13408-020-00100-0. [PDF]

### 2020

- Creaser J, Ashwin P, Tsaneva-Atanasova K. (2020) Sequential Escapes and Synchrony Breaking for Networks of Bistable Oscillatory Nodes,
*SIAM Journal on Applied Dynamical Systems*, volume 19, no. 4, pages 2829-2846, DOI:10.1137/20m1345773. [PDF] - Alkhayuon H, Ashwin P. (2020) Weak tracking in nonautonomous chaotic systems,
*Physical Review E*, volume 102, no. 5, article no. 052210, DOI:10.1103/physreve.102.052210. [PDF] - Cooper FC, Dueben PD, Denis C, Dawson A, Ashwin P. (2020) The Relationship between Numerical Precision and Forecast Lead Time in the Lorenz'95 System,
*MONTHLY WEATHER REVIEW*, volume 148, no. 2, pages 849-855, DOI:10.1175/MWR-D-18-0200.1. [PDF] - White RR, Lin C, Leaves I, Castro IG, Metz J, Bateman BC, Botchway SW, Ward AD, Ashwin P, Sparkes I. (2020) Miro2 tethers the ER to mitochondria to promote mitochondrial fusion in tobacco leaf epidermal cells,
*Commun Biol*, volume 3, no. 1, DOI:10.1038/s42003-020-0872-x. [PDF] - Ceni A, Ashwin P, Livi L, Postlethwaite C. (2020) The echo index and multistability in input-driven recurrent neural networks,
*Physica D: Nonlinear Phenomena*, volume 412, DOI:10.1016/j.physd.2020.132609. - Nyman KHM, Ashwin P, Ditlevsen PD. (2020) Bifurcation of critical sets and relaxation oscillations in singular fast-slow systems,
*Nonlinearity*, volume 33, no. 6, pages 2853-2904, DOI:10.1088/1361-6544/ab7292. [PDF] - Ashwin P, Castro SBSD, Lohse A. (2020) Almost Complete and Equable Heteroclinic Networks,
*Journal of Nonlinear Science*, volume 30, no. 1, pages 1-22, DOI:10.1007/s00332-019-09566-z. - Ceni A, Ashwin P, Livi L. (2020) Interpreting Recurrent Neural Networks Behaviour via Excitable Network Attractors,
*Cognitive Computation*, volume 12, no. 2, pages 330-356, DOI:10.1007/s12559-019-09634-2. - Ashwin P, Goetz A, Peres P, Rodrigues A. (2020) Embeddings of interval exchange transformations into planar piecewise isometries,
*Ergodic Theory and Dynamical Systems*, volume 40, no. 5, pages 1153-1179, DOI:10.1017/etds.2018.112.

### 2019

- Ashwin P, von der Heydt AS. (2019) Extreme Sensitivity and Climate Tipping Points,
*Journal of Statistical Physics*, volume 179, no. 5-6, pages 1531-1552, DOI:10.1007/s10955-019-02425-x. [PDF] - Ashwin P, Bick C, Poignard C. (2019) State-dependent effective interactions in oscillator networks through coupling functions with dead zones,
*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, volume 377, no. 2160, pages 20190042-20190042, DOI:10.1098/rsta.2019.0042. [PDF] - Ceni A, Ashwin P, Livi L. (2019) Interpreting Recurrent Neural Networks Behaviour via Excitable Network Attractors,
*Cognitive Computation*, volume 12, no. 2, pages 330-356, DOI:10.1007/s12559-019-09634-2. [PDF] - Alkhayuon H, Ashwin P, Jackson LC, Quinn C, Wood RA. (2019) Basin bifurcations, oscillatory instability and rate-induced thresholds for Atlantic meridional overturning circulation in a global oceanic box model,
*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, volume 475, no. 2225, DOI:10.1098/rspa.2019.0051. - Perez-Cervera A, Ashwin P, Huguet G, Seara TM, Rankin J. (2019) The uncoupling limit of identical Hopf bifurcations with an application to perceptual bistability,
*JOURNAL OF MATHEMATICAL NEUROSCIENCE*, volume 9, article no. ARTN 7, DOI:10.1186/s13408-019-0075-2. [PDF]

### 2018

- Smug D, Ashwin P, Sornette D. (2018) Predicting financial market crashes using ghost singularities,
*PLOS ONE*, volume 13, no. 3, pages e0195265-e0195265, DOI:10.1371/journal.pone.0195265. [PDF] - Thoubaan M, Ashwin P. (2018) Existence and stability of chimera states in a minimal system of phase oscillators,
*Chaos: An Interdisciplinary Journal of Nonlinear Science*, DOI:10.1063/1.5044750. - Ditlevsen PD, Ashwin P. (2018) Complex climate response to astronomical forcing: The middle-pleistocene transition in glacial cycles and changes in frequency locking,
*Frontiers in Physics*, volume 6, no. JUN, DOI:10.3389/fphy.2018.00062. - Smug D, Sornette D, Ashwin PB. (2018) A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises),
*International Journal of Bifurcation and Chaos*, volume 28, pages 1830010-1830010, DOI:10.1142/S0218127418300100. - Ashwin P, David Camp C, von der Heydt AS. (2018) Chaotic and non-chaotic response to quasiperiodic forcing: limits to predictability of ice ages paced by Milankovitch forcing,
*Dynamics and Statistics of the Climate System*, volume 3, no. 1, DOI:10.1093/climsys/dzy002. [PDF] - Ashwin P, Creaser J, Tsaneva-Atanasova K. (2018) Sequential escapes: onset of slow domino regime via a saddle connection,
*EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS*, volume 227, no. 10-11, pages 1091-1100, DOI:10.1140/epjst/e2018-800038-5. [PDF] - Smug D, Ashwin P, Sornette D. (2018) Predicting financial market crashes using ghost singularities,
*PLoS One*, volume 13, no. 3, DOI:10.1371/journal.pone.0195265. [PDF] - Ashwin P, Postlethwaite C. (2018) Sensitive Finite-State Computations Using a Distributed Network With a Noisy Network Attractor,
*IEEE Transactions on Neural Networks and Learning Systems*, volume 29, no. 12, pages 5847-5858, DOI:10.1109/TNNLS.2018.2813404. - Alkhayuon HM, Ashwin P. (2018) Rate-induced tipping from periodic attractors: Partial tipping and connecting orbits,
*Chaos*, volume 28, no. 3, DOI:10.1063/1.5000418. - Weinberger O, Ashwin P. (2018) From coupled networks of systems to networks of states in phase space,
*Discrete and Continuous Dynamical Systems - Series B*, volume 23, no. 5, pages 2021-2041, DOI:10.3934/dcdsb.2018193. - Creaser J, Tsaneva-Atanasova K, Ashwin P. (2018) Sequential Noise-Induced Escapes for Oscillatory Network Dynamics,
*SIAM Journal on Applied Dynamical Systems*, volume 17, no. 1, pages 500-525, DOI:10.1137/17m1126412. [PDF]

### 2017

- Smug D, Sornette D, Ashwin P. (2017) A Generalized 2D-Dynamical Mean-Field Ising Model with a Rich Set of Bifurcations (Inspired and Applied to Financial Crises), DOI:10.2139/ssrn.3064673.
- Newton AJH, Seidenstein AH, McDougal RA, Pérez-Cervera A, Huguet G, M-Seara T, Haimerl C, Angulo-Garcia D, Torcini A, Cossart R. (2017) 26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3,
*BMC Neuroscience*, volume 18, no. S1, article no. 60, DOI:10.1186/s12868-017-0372-1. [PDF] - Ashwin P, Creaser J, Tsaneva-Atanasova K. (2017) Fast and slow domino regimes in transient network dynamics,
*PHYSICAL REVIEW E*, volume 96, no. 5, article no. ARTN 052309, DOI:10.1103/PhysRevE.96.052309. [PDF] - Lin C, White RR, Sparkes I, Ashwin PB. (2017) Modelling endoplasmic reticulum network maintenance in a plant cell,
*Biophysical Journal*, volume 113, pages 214-222, DOI:10.1016/j.bpj.2017.05.046. - von der Heydt AS, Ashwin P. (2017) State dependence of climate sensitivity: attractor constraints and palaeoclimate regimes,
*Dynamics and Statistics of the Climate System*, volume 1, no. 1, DOI:10.1093/climsys/dzx001. [PDF] - Ashwin P, Perryman C, Wieczorek S. (2017) Parameter shifts for nonautonomous systems in low dimension: Bifurcation- and rate-induced tipping,
*Nonlinearity*, volume 30, no. 6, pages 2185-2210, DOI:10.1088/1361-6544/aa675b.

### 2016

- von der Heydt AS, Dijkstra HA, van de Wal RSW, Caballero R, Crucifix M, Foster GL, Huber M, Köhler P, Rohling E, Valdes PJ. (2016) Lessons on Climate Sensitivity From Past Climate Changes,
*Current Climate Change Reports*, volume 2, no. 4, pages 148-158, DOI:10.1007/s40641-016-0049-3. [PDF] - Ashwin P, Rodrigues A. (2016) Hopf normal form with
SN symmetry and reduction to systems of nonlinearly coupled phase oscillators,*Physica D: Nonlinear Phenomena*, volume 325, pages 14-24, DOI:10.1016/j.physd.2016.02.009. - Lin C, Schuster M, Guimaraes SC, Ashwin P, Schrader M, Metz J, Hacker C, Gurr SJ, Steinberg G. (2016) Active diffusion and microtubule-based transport oppose myosin forces to position organelles in cells,
*NATURE COMMUNICATIONS*, volume 7, article no. ARTN 11814, DOI:10.1038/ncomms11814. [PDF] - Bick C, Ashwin P, Rodrigues A. (2016) Chaos in generically coupled phase oscillator networks with nonpairwise interactions,
*Chaos: An Interdisciplinary Journal of Nonlinear Science*, volume 26, no. 9, DOI:10.1063/1.4958928. [PDF] - Ashwin P, Bick C, Burylko O. (2016) Identical Phase Oscillator Networks: Bifurcations, Symmetry and Reversibility for Generalized Coupling,
*Frontiers in Applied Mathematics and Statistics*, volume 2, DOI:10.3389/fams.2016.00007. [PDF] - Ashwin P, Postlethwaite C. (2016) Quantifying noisy attractors: From heteroclinic to excitable networks,
*SIAM Journal on Applied Dynamical Systems*, volume 15, no. 4, pages 1989-2016, DOI:10.1137/16M1061813. - Roslan UAM, Ashwin P. (2016) Local and global stability indices for a riddled basin attractor of a piecewise linear map,
*Dynamical Systems*, volume 31, no. 3, pages 375-392, DOI:10.1080/14689367.2016.1148662. [PDF] - Bick C, Ashwin P. (2016) Chaotic weak chimeras and their persistence in coupled populations of phase oscillators,
*Nonlinearity*, volume 29, no. 5, pages 1468-1486, DOI:10.1088/0951-7715/29/5/1468. - Panaggio MJ, Abrams DM, Ashwin P, Laing CR. (2016) Chimera states in networks of phase oscillators: The case of two small populations,
*Physical Review E*, volume 93, no. 1, DOI:10.1103/PhysRevE.93.012218. - Ashwin P, Coombes S, Nicks R. (2016) Mathematical Frameworks for Oscillatory Network Dynamics in Neuroscience,
*Journal of Mathematical Neuroscience*, volume 6, no. 1, pages 1-92, DOI:10.1186/s13408-015-0033-6. - Ashwin P, Postlethwaite C. (2016) Designing Heteroclinic and Excitable Networks in Phase Space Using Two Populations of Coupled Cells,
*Journal of Nonlinear Science*, volume 26, no. 2, pages 345-364, DOI:10.1007/s00332-015-9277-2.

### 2015

- Ashwin P, Zaikin A. (2015) Pattern selection: the importance of "how you get there",
*Biophys J*, volume 108, no. 6, pages 1307-1308, DOI:10.1016/j.bpj.2015.01.036. [PDF] - Ashwin P, Ditlevsen P. (2015) The middle Pleistocene transition as a generic bifurcation on a slow manifold,
*CLIMATE DYNAMICS*, volume 45, no. 9-10, pages 2683-2695, DOI:10.1007/s00382-015-2501-9. [PDF] - Ismail A, Ashwin P. (2015) Multi-cluster dynamics in coupled phase oscillator networks,
*DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL*, volume 30, no. 1, pages 122-135, DOI:10.1080/14689367.2014.984917. [PDF] - Ashwin P, Burylko O. (2015) Weak chimeras in minimal networks of coupled phase oscillators,
*Chaos*, volume 25, no. 1, DOI:10.1063/1.4905197.

### 2014

- Lin C, Zhang Y, Sparkes I, Ashwin P. (2014) Structure and dynamics of ER: minimal networks and biophysical constraints,
*Biophys J*, volume 107, no. 3, pages 763-772, DOI:10.1016/j.bpj.2014.06.032. [PDF] - Higuchi Y, Ashwin P, Roger Y, Steinberg G. (2014) Early endosome motility spatially organizes polysome distribution,
*J Cell Biol*, volume 204, no. 3, pages 343-357, DOI:10.1083/jcb.201307164. [PDF]

### 2013

- Wright CD, Diosdado JAV, Wang L, Liu Y, Ashwin P, Kohary KI, Aziz MM, Hosseini P, Hicken RJ, Cassinerio M. (2013) Nanosession: Phase Change Memories,
*Frontiers in Electronic Materials*, Wiley, 163-176, DOI:10.1002/9783527667703.ch38. - Hobbs C, Ashwin P, Wieczorek S, Vitolo R, Cox P. (2013) Erratum: Tipping points in open systems: Bifurcation, noise-included and rate-dependent examples in the climate system (Philosophical Transactions of the Royal Society A (2012) 370 (1166-1184) DOI: 10.1098/rsta.2011.0306),
*Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences*, volume 371, no. 1994, DOI:10.1098/rsta.2013.0098. - Diosdado JAV, Ashwin P, Kohary KI, Wright CD. (2013) Response to "comment on 'Threshold switching via electric field induced crystallization in phase change memory devices'" [Appl. Phys. Lett. 102, 236101 (2012)],
*Applied Physics Letters*, volume 102, no. 23, DOI:10.1063/1.4809722. - Lin C, Ashwin P, Steinberg G. (2013) Motor-mediated bidirectional transport along an antipolar microtubule bundle: A mathematical model,
*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, volume 87, no. 5, DOI:10.1103/PhysRevE.87.052709. - Ashwin P, Postlethwaite C. (2013) On designing heteroclinic networks from graphs,
*Physica D: Nonlinear Phenomena*, volume 265, pages 26-39, DOI:10.1016/j.physd.2013.09.006.

### 2012

- Glendinning P, Ashwin P, Broomhead D, Callard R, Nicol M, Sturman R. (2012) Untitled,
*DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL*, volume 27, no. 1, pages 1-9, DOI:10.1080/14689367.2012.664405. [PDF] - Wright CD, Wang L, Aziz MM, Diosdado JAV, Ashwin P. (2012) Phase-change processors, memristors and memflectors,
*Physica Status Solidi (B) Basic Research*, volume 249, no. 10, pages 1978-1984, DOI:10.1002/pssb.201200378. - Kohary K, Vazquez-Diosdado J, Ashwin P, Wright CD. (2012) Role of enthalpy and relative electric permittivity in electric field induced nucleation,
*Materials Research Society Symposium Proceedings*, volume 1431, pages 37-42, DOI:10.1557/opl.2012.1405. - Kohary K, Diosdado JAV, Ashwin P, Wright CD. (2012) Electric-field-assisted crystallisation in phase-change materials,
*Physica Status Solidi (B) Basic Research*, volume 249, no. 10, pages 1897-1901, DOI:10.1002/pssb.201200376. - Diosdado JAV, Ashwin P, Kohary KI, Wright CD. (2012) Threshold switching via electric field induced crystallization in phase-change memory devices,
*APPLIED PHYSICS LETTERS*, volume 100, no. 25, article no. ARTN 253105, DOI:10.1063/1.4729551. [PDF] - Benjamin O, Fitzgerald THB, Ashwin P, Tsaneva-Atanasova K, Chowdhury F, Richardson MP, Terry JR. (2012) A phenomenological model of seizure initiation suggests network structure may explain seizure frequency in idiopathic generalised epilepsy,
*Journal of Mathematical Neuroscience*, volume 2, no. 1, DOI:10.1186/2190-8567-2-1. - Ashwin P, Wieczorek S, Vitolo R, Cox P. (2012) Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system,
*PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES*, volume 370, no. 1962, pages 1166-1184, DOI:10.1098/rsta.2011.0306. [PDF]

### 2011

- ASHWIN P. (2011) SYMMETRIC DYNAMICS AND ELECTRONIC CIRCUITS,
*Nonlinear Dynamics in Circuits*, World Scientific Publishing, 35-53, DOI:10.1142/9789812830609_0002. - Ashwin P, Karabacak O, Nowotny T. (2011) Criteria for robustness of heteroclinic cycles in neural microcircuits,
*J Math Neurosci*, volume 1, no. 1, DOI:10.1186/2190-8567-1-13. [PDF] - Ashwin P, Karabacak O. (2011) Robust Heteroclinic Behaviour, Synchronization, and Ratcheting of Coupled Oscillators,
*DYNAMICS, GAMES AND SCIENCE II*, volume 2, pages 125-140, DOI:10.1007/978-3-642-14788-3_10. [PDF] - Belmont MR, Ashwin P. (2011) The independent variable interpolation technique for nonuniformly sampled shallow-angle lidar data,
*Journal of Atmospheric and Oceanic Technology*, volume 28, no. 12, pages 1672-1678, DOI:10.1175/JTECH-D-11-00037.1. - Bick C, Timme M, Paulikat D, Rathlev D, Ashwin P. (2011) Chaos in Symmetric Phase Oscillator Networks,
*PHYSICAL REVIEW LETTERS*, volume 107, no. 24, article no. ARTN 244101, DOI:10.1103/PhysRevLett.107.244101. [PDF] - Lin C, Steinberg G, Ashwin P. (2011) Bidirectional transport and pulsing states in a multi-lane ASEP model,
*JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT*, article no. ARTN P09027, DOI:10.1088/1742-5468/2011/09/P09027. [PDF] - Schuster M, Kilaru S, Ashwin P, Lin C, Severs NJ, Steinberg G. (2011) Controlled and stochastic retention concentrates dynein at microtubule ends to keep endosomes on track,
*EMBO J*, volume 30, no. 4, pages 652-664, DOI:10.1038/emboj.2010.360. [PDF] - Karabacak O, Ashwin P. (2011) On statistical attractors and the convergence of time averages,
*Mathematical Proceedings of the Cambridge Philosophical Society*, volume 150, no. 2, pages 353-365, DOI:10.1017/S0305004110000642. - Aguiar M, Ashwin P, Dias A, Field M. (2011) Dynamics of Coupled Cell Networks: Synchrony, Heteroclinic Cycles and Inflation,
*JOURNAL OF NONLINEAR SCIENCE*, volume 21, no. 2, pages 271-323, DOI:10.1007/s00332-010-9083-9. [PDF] - Podvigina O, Ashwin P. (2011) On local attraction properties and a stability index for heteroclinic connections,
*NONLINEARITY*, volume 24, no. 3, pages 887-929, DOI:10.1088/0951-7715/24/3/009. [PDF] - Wieczorek S, Ashwin P, Luke CM, Cox PM. (2011) Excitability in ramped systems: the compost-bomb instability,
*PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES*, volume 467, no. 2129, pages 1243-1269, DOI:10.1098/rspa.2010.0485. [PDF]

### 2010

- Wright CD, Ashawaraya S, Ashwin P, Aziz MM, Hicken RJ, Kohary K, Liu Y, Marmier ASH, Shah P, Vazquez Diosdado J. (2010) Phase-change technologies: from PCRAM to probe-storage to processors,
*European Phase Change and Ovonics Science Symposium 2010*. [PDF] - Ashwin P, Orosz G, Borresen J. (2010) Heteroclinic switching in coupled oscillator networks: Dynamics on odd graphs,
*Understanding Complex Systems*, volume 2010, pages 31-50, DOI:10.1007/978-3-642-04629-2_3. - Vazquez J, Ashwin P, Kohary KI, Wright CD. (2010) Phase-change RAM modelling and design via a Gillespie-type cellular automata approach,
*2010 IEEE International Conference on Electronics, Circuits, and Systems, ICECS 2010 - Proceedings*, pages 1013-1016, DOI:10.1109/ICECS.2010.5724686. - Ashwin P, Lin C, Steinberg G. (2010) Queueing induced by bidirectional motor motion near the end of a microtubule,
*PHYSICAL REVIEW E*, volume 82, no. 5, article no. ARTN 051907, DOI:10.1103/PhysRevE.82.051907. [PDF] - Chawanya T, Ashwin P. (2010) A minimal system with a depth-two heteroclinic network,
*Dynamical Systems*, volume 25, no. 3, pages 397-412, DOI:10.1080/14689367.2010.500102. - Afraimovich V, Ashwin P, Kirk V. (2010) Robust heteroclinic and switching dynamics,
*Dynamical Systems*, volume 25, no. 3, pages 285-286, DOI:10.1080/14689367.2010.522390. - Ashwin P, Podvigina O. (2010) Noise-induced switching near a depth two heteroclinic network and an application to Boussinesq convection,
*Chaos*, volume 20, no. 2, DOI:10.1063/1.3439320. - al Azad AK, Ashwin P. (2010) Within-Burst Synchrony Changes for Coupled Elliptic Bursters,
*SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS*, volume 9, no. 1, pages 261-281, DOI:10.1137/090746045. [PDF] - Ashwin P, Lavric A. (2010) A low-dimensional model of binocular rivalry using winnerless competition,
*PHYSICA D-NONLINEAR PHENOMENA*, volume 239, no. 9, pages 529-536, DOI:10.1016/j.physd.2009.06.018. [PDF] - Ashwin P, Goetz A. (2010) Cone exchange transformations and boundedness of orbits,
*Ergodic Theory and Dynamical Systems*, volume 30, no. 5, pages 1311-1330, DOI:10.1017/S0143385709000625. - Karabacak O, Ashwin P. (2010) Heteroclinic Ratchets in Networks of Coupled Oscillators,
*JOURNAL OF NONLINEAR SCIENCE*, volume 20, no. 1, pages 105-129, DOI:10.1007/s00332-009-9053-2. [PDF]

### 2009

- Orosz G, Moehlis J, Ashwin P. (2009) Designing the dynamics of globally coupled oscillators,
*Progress of Theoretical Physics*, volume 122, no. 3, pages 611-630, DOI:10.1143/PTP.122.611. - Ashwin P, Fu X, Lin C. (2009) On planar piecewise and two-torus parabolic maps,
*International Journal of Bifurcation and Chaos*, volume 19, no. 7, pages 2383-2390, DOI:10.1142/S0218127409024153. - Orosz G, Ashwin P, Townley S. (2009) Learning of spatio-temporal codes in a coupled oscillator system,
*IEEE Trans Neural Netw*, volume 20, no. 7, pages 1135-1147, DOI:10.1109/TNN.2009.2016658. [PDF]

### 2008

- Wordsworth J, Ashwin P. (2008) Spatiotemporal coding of inputs for a system of globally coupled phase oscillators,
*PHYSICAL REVIEW E*, volume 78, no. 6, article no. ARTN 066203, DOI:10.1103/PhysRevE.78.066203. [PDF] - Trovati M, Ashwin P, Byott N. (2008) Packings induced by piecewise isometries cannot contain the Arbelos,
*DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS*, volume 22, no. 3, pages 791-806. [PDF] - Ashwin P, Patnaik BSV, Wright CD. (2008) Fast simulation of phase-change processes in chalcogenide alloys using a Gillespie-type cellular automata approach,
*JOURNAL OF APPLIED PHYSICS*, volume 104, no. 8, article no. ARTN 084901, DOI:10.1063/1.2978334. [PDF] - Ashwin P, Burylko O, Maistrenko Y. (2008) Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators,
*Physica D: Nonlinear Phenomena*, volume 237, no. 4, pages 454-466, DOI:10.1016/j.physd.2007.09.015.

### 2007

- Podvigina O, Ashwin P. (2007) The 1 : sqrt(2) mode interaction and heteroclinic networks in Boussinesq convection,
*Physica D: Nonlinear Phenomena*, volume 234, no. 1, pages 23-48, DOI:10.1016/j.physd.2007.06.024. - Ashwin P, Orosz G, Wordsworth J, Townley S. (2007) Dynamics on networks of cluster states for globally coupled phase oscillators,
*SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS*, volume 6, no. 4, pages 728-758, DOI:10.1137/070683969. [PDF] - Wright CD, Blyuss K, Ashwin P. (2007) Master-equation approach to understanding multistate phase-change memories and processors,
*APPLIED PHYSICS LETTERS*, volume 90, no. 6, article no. ARTN 063113, DOI:10.1063/1.2475606. [PDF] - Orosz G, Ashwin P, Wordsworth J, Townley S. (2007) Cluster synchronization, switching and spatio-temporal coding in a phase oscillator network,
*Proceedings of Applied Mathematics and Mechanics*, volume 7, pages 1030703-1030704. [PDF] - Ashwin P, Orosz G, Wordsworth J, Townley S. (2007) Dynamics on networks of cluster states for globally coupled phase oscillators,
*SIAM Journal on Applied Dynamical Systems*, volume 6, pages 728-758. [PDF] - Trovati M, Ashwin P. (2007) Tangency properties of a pentagonal tiling generated by a piecewise isometry,
*Chaos*, volume 17, no. 4, DOI:10.1063/1.2825291. [PDF]

### 2006

- Ashwin P, Burylko O, Maistrenko Y, Popovych O. (2006) Extreme sensitivity to detuning for globally coupled phase oscillators,
*PHYSICAL REVIEW LETTERS*, volume 96, no. 5, article no. ARTN 054102, DOI:10.1103/PhysRevLett.96.054102. [PDF] - Ashwin P, Goetz A. (2006) Polygonal invariant curves for a planar piecewise isometry,
*TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY*, volume 358, no. 1, pages 373-390, DOI:10.1090/S0002-9947-05-03670-6. [PDF] - Podvigina O, Ashwin P, Hawker D. (2006) Modelling instability of
*ABC*flow using a mode interaction between steady and Hopf bifurcations with rotational symmetries of the cube,*PHYSICA D-NONLINEAR PHENOMENA*, volume 215, no. 1, pages 62-79, DOI:10.1016/j.physd.2006.01.010. [PDF] - Blyuss KB, Ashwin P, Wright CD, Bassom AP. (2006) Front propagation in a phase field model with phase-dependent heat absorption,
*PHYSICA D-NONLINEAR PHENOMENA*, volume 215, no. 2, pages 127-136, DOI:10.1016/j.physd.2006.01.024. [PDF]

### 2005

- Ashwin P, Field M. (2005) Product dynamics for homoclinic attractors,
*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, volume 461, no. 2053, pages 155-177, DOI:10.1098/rspa.2004.1362. - Ashwin P, Timme M. (2005) Nonlinear dynamics: when instability makes sense,
*Nature*, volume 436, no. 7047, pages 36-37, DOI:10.1038/436036b. [PDF] - Ashwin P. (2005) Riddled basins and coupled dynamical systems,
*Dynamics of Coupled Map Lattices and of Related Spatially Extended Systems*, Springer, 181-207. [PDF] - Ashwin P, Dangelmayr G. (2005) Reduced dynamics and symmetric solutions for globally coupled weakly dissipative oscillators,
*Dynamical Systems*, volume 20, no. 3, pages 333-367, DOI:10.1080/14689360500151813. - Ashwin P, Goetz A. (2005) Invariant curves and explosion of periodic Islands in systems of piecewise rotations,
*SIAM Journal on Applied Dynamical Systems*, volume 4, no. 2, pages 437-458, DOI:10.1137/040605394. - Ashwin P, Timme M. (2005) Unstable attractors: existence and robustness in networks of oscillators with delayed pulse coupling,
*NONLINEARITY*, volume 18, no. 5, pages 2035-2060, DOI:10.1088/0951-7715/18/5/009. [PDF] - Hawker D, Ashwin P. (2005) Classification of robust heteroclinic cycles for vector fields in ℝ
^{3}with symmetry,*Journal of Physics A: Mathematical and General*, volume 38, no. 39, pages 8319-8335, DOI:10.1088/0305-4470/38/39/002. - Blyuss KB, Ashwin P, Bassom AP, Wright CD. (2005) Master-equation approach to the study of phase-change processes in data storage media,
*PHYSICAL REVIEW E*, volume 72, no. 1, article no. ARTN 011607, DOI:10.1103/PhysRevE.72.011607. [PDF] - Hawker D, Ashwin P. (2005) Robust bursting to the origin; heteroclinic cycles with maximal symmetry equilibria,
*International Journal of Bifurcation and Chaos in Applied Sciences and Engineering*, volume 15, no. 9, pages 2819-2832, DOI:10.1142/S0218127405013708. - Ashwin P, Borresen J. (2005) Discrete computation using a perturbed heteroclinic network,
*Physics Letters, Section A: General, Atomic and Solid State Physics*, volume 347, no. 4-6, pages 208-214, DOI:10.1016/j.physleta.2005.08.013.

### 2004

- Ashwin P, Borresen J. (2004) Encoding via conjugate symmetries of slow oscillations for globally coupled oscillators,
*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, volume 70, no. 2 2, DOI:10.1103/PhysRevE.70.026203. - Ashwin P, Rucklidge AM, Sturman R. (2004) Cycling chaotic attractors in two models for dynamics with invariant subspaces,
*Chaos*, volume 14, no. 3, pages 571-582, DOI:10.1063/1.1769111. [PDF] - Ashwin P, Rucklidge AM, Sturman R. (2004) Two-state intermittency near a symmetric interaction of saddle-node and Hopf bifurcations: A case study from dynamo theory,
*Physica D: Nonlinear Phenomena*, volume 194, no. 1-2, pages 30-48, DOI:10.1016/j.physd.2004.02.002. - Sturman R, Ashwin P. (2004) Internal dynamics of intermittency,
*"Dynamics and Bifurcation of Patterns in Dissipative Systems, World Scientific Series on Nonlinear Science 12, World Scientific, Singapore"*.

### 2003

- Ashwin P. (2003) THE SYMMETRY PERSPECTIVE: FROM EQUILIBRIUM TO CHAOS IN PHASE SPACE AND PHYSICAL SPACE (Progress in Mathematics 200),
*Bulletin of the London Mathematical Society*, volume 35, no. 3, pages 430-432, DOI:10.1112/s0024609303262081. - Ashwin P, Field M, Rucklidge AM, Sturman R. (2003) Phase resetting effects for robust cycles between chaotic sets,
*Chaos*, volume 13, no. 3, pages 973-981, DOI:10.1063/1.1586531. [PDF] - Ashwin P, Rucklidge AM, Sturman R. (2003) Cycling attractors of coupled cell systems and dynamics with symmetry,
*SYNCHRONIZATION: THEORY AND APPLICATION*, volume 109, pages 5-23. [PDF] - Ashwin P, Podvigina O. (2003) Hopf bifurcation with cubic symmetry and instability of ABC flow,
*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, volume 459, no. 2035, pages 1801-1827, DOI:10.1098/rspa.2002.1090. - Ashwin P. (2003) Nonlinear dynamics: Synchronization from chaos,
*Nature*, volume 422, no. 6930, pages 384-385, DOI:10.1038/422384a. [PDF] - Ashwin P, Sturman R. (2003) Decelerating defects and non-ergodic critical behaviour in a unidirectionally coupled map lattice,
*Physics Letters, Section A: General, Atomic and Solid State Physics*, volume 309, no. 5-6, pages 423-434, DOI:10.1016/S0375-9601(03)00245-7. - Ashwin P, Fu XC, Deane J. (2003) Properties of the invariant disk packing in a model bandpass sigma-delta modulator,
*International Journal of Bifurcation and Chaos in Applied Sciences and Engineering*, volume 13, no. 3, pages 631-641, DOI:10.1142/S0218127403006753. - Ashwin P. (2003) Patchwork patterns: Dynamics on unbounded domains,
*Bifurcation, Symmetry and Patterns*, Porto,*Trends in Mathematics*, no. Trennds in Mathematics, pages 67-74. [PDF] - Fu XC, Ashwin P. (2003) Symbolic analysis for some planar piecewise linear maps,
*DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS*, volume 9, no. 6, pages 1533-1548, DOI:10.3934/dcds.2003.9.1533. [PDF] - Ashwin P, Ochs G. (2003) Convergence to local random attractors,
*Dynamical Systems*, volume 18, no. 2, pages 139-158, DOI:10.1080/1468936031000102727.

### 2002

- Ashwin P, Rucklidge AM, Sturman R. (2002) Infinities of stable periodic orbits in systems of coupled oscillators,
*Phys Rev E Stat Nonlin Soft Matter Phys*, volume 66, no. 3 Pt 2A, DOI:10.1103/PhysRevE.66.035201. [PDF] - Ashwin P, Montaldi J. (2002) Group theoretic conditions for existence of robust relative homoclinic trajectories,
*MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY*, volume 133, pages 125-141, DOI:10.1017/S0305004101005801. [PDF] - Ashwin P, Nicol M, Kirkby N. (2002) Acceleration of one-dimensional mixing by discontinuous mappings,
*Physica A: Statistical Mechanics and its Applications*, volume 310, no. 3-4, pages 347-363, DOI:10.1016/S0378-4371(02)00774-4. - Ashwin P, Fu XC. (2002) On the geometry of orientation-preserving planar piecewise isometries,
*JOURNAL OF NONLINEAR SCIENCE*, volume 12, no. 3, pages 207-240, DOI:10.1007/s00332-002-0477-1. [PDF] - Ashwin P, Fu XC. (2002) On the dynamics of some nonhyperbolic area-preserving piecewise linear maps,
*MATHEMATICS IN SIGNAL PROCESSING V*, no. 71, pages 137-145. [PDF] - Ashwin P, Bartuccelli MV, Bridges TJ, Gourley SA. (2002) Travelling fronts for the KPP equation with spatio-temporal delay,
*Zeitschrift fur Angewandte Mathematik und Physik*, volume 53, no. 1, pages 103-122, DOI:10.1007/s00033-002-8145-8. - Fu X-C, Lu W, Ashwin P, Duan J. (2002) Symbolic representation of iterated maps,
*Topological Methods in Nonlinear Analysis*, volume 18, pages 119-147. - Ashwin P, Fu XC, Terry JR. (2002) Riddling and invariance for discontinuous maps preserving Lebesgue measure,
*Nonlinearity*, volume 15, no. 3, pages 633-645, DOI:10.1088/0951-7715/15/3/306.

### 2001

- Fu X-C, Lu W, Ashwin P, Duan J. (2001) Symbolic representations of iterated maps,
*Topological Methods in Nonlinear Analysis*, volume 18, no. 1, DOI:10.12775/tmna.2001.027. - Ashwin P, Deane JHB, Fu XC. (2001) Dynamics of a bandpass sigma-delta modulator as a piecewise isometry,
*ISCAS 2001 - 2001 IEEE International Symposium on Circuits and Systems, Conference Proceedings*, volume 3, pages 811-814, DOI:10.1109/ISCAS.2001.921456. - Covas E, Tavakol R, Ashwin P, Tworkowski A, Brooke JM. (2001) In-out intermittency in partial differential equation and ordinary differential equation models,
*Chaos*, volume 11, no. 2, pages 404-409, DOI:10.1063/1.1374243. [PDF] - Ashwin P, Melbourne I, Nicol M. (2001) Hypermeander of spirals: Local bifurcations and statistical properties,
*Physica D: Nonlinear Phenomena*, volume 156, no. 3-4, pages 364-382, DOI:10.1016/S0167-2789(01)00296-2. - Ashwin P, Breakspear M. (2001) Anisotropic properties of riddled basins,
*Physics Letters, Section A: General, Atomic and Solid State Physics*, volume 280, no. 3, pages 139-145, DOI:10.1016/S0375-9601(01)00043-3. - Nicol M, Melbourne I, Ashwin P. (2001) Euclidean extensions of dynamical systems,
*NONLINEARITY*, volume 14, no. 2, pages 275-300, DOI:10.1088/0951-7715/14/2/306. [PDF] - Ashwin P, Fu XC. (2001) Tangencies in invariant disc packings for certain planar piecewise isometries are rare,
*Dynamical Systems*, volume 16, no. 4, pages 333-345, DOI:10.1080/14689360110073650. - Ashwin P, Covas E, Tavakol R. (2001) Influence of noise on scalings for in-out intermittency,
*Phys Rev E Stat Nonlin Soft Matter Phys*, volume 64, no. 6 Pt 2, DOI:10.1103/PhysRevE.64.066204. [PDF]

### 2000

- Ashwin P, Fu XC, Nishikawa T, Zyczkowski K. (2000) Invariant sets for discontinuous parabolic area-preserving torus maps,
*NONLINEARITY*, volume 13, no. 3, pages 819-835, DOI:10.1088/0951-7715/13/3/317. [PDF] - Ashwin P, Dangelmayr G. (2000) Isochronicity-induced bifurcations in systems of weakly dissipative coupled oscillators,
*Dynamical Systems*, volume 15, no. 3, pages 263-286, DOI:10.1080/713603745. - Ashwin P, Terry JR. (2000) On riddling and weak attractors,
*Physica D: Nonlinear Phenomena*, volume 142, no. 1-2, pages 87-100, DOI:10.1016/S0167-2789(00)00062-2. - Terry JR, Ashwin P. (2000) Comment on "Riddling of chaotic sets in periodic windows",
*Phys Rev Lett*, volume 85, no. 2, DOI:10.1103/PhysRevLett.85.472. [PDF]

### 1999

- Ashwin P. (1999) Chaotic Intermittency of Patterns in Symmetric Systems,
*Pattern Formation in Continuous and Coupled Systems*, Springer Nature, 11-24, DOI:10.1007/978-1-4612-1558-5_2. - Ashwin P, Covas E, Tavakol R. (1999) Transverse instability for non-normal parameters,
*NONLINEARITY*, volume 12, no. 3, pages 563-577, DOI:10.1088/0951-7715/12/3/009. [PDF] - Deane JHB, Ashwin P, Hamill DC, Jefferies DJ. (1999) Calculation of the periodic spectral components in a chaotic DC-DC converter,
*IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications*, volume 46, no. 11, pages 1313-1319, DOI:10.1109/81.802818. - Ashwin P. (1999) Minimal attractors and bifurcations of random dynamical systems,
*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*, volume 455, no. 1987, pages 2615-2634, DOI:10.1098/rspa.1999.0419. - Terry JR, Thornburg KS, DeShazer DJ, VanWiggeren GD, Zhu S, Ashwin P, Roy R. (1999) Synchronization of chaos in an array of three lasers,
*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, volume 59, no. 4, pages 4036-4043, DOI:10.1103/PhysRevE.59.4036. - Ashwin P. (1999) Attractors of a randomly forced electronic oscillator,
*Physica D: Nonlinear Phenomena*, volume 125, no. 3-4, pages 302-310, DOI:10.1016/S0167-2789(98)00259-0. - Ashwin P, Melbourne I, Nicol M. (1999) Drift bifurcations of relative equilibria and transitions of spiral waves,
*Nonlinearity*, volume 12, no. 4, pages 741-755, DOI:10.1088/0951-7715/12/4/301. - Ashwin P, Field M. (1999) Heteroclinic networks in coupled cell systems,
*Archive for Rational Mechanics and Analysis*, volume 148, no. 2, pages 107-143, DOI:10.1007/s002050050158.

### 1998

- Ashwin P. (1998) Non-linear dynamics, loss of synchronization and symmetry breaking,
*Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering*, volume 212, no. 3, pages 183-187, DOI:10.1243/0954410981532252. - Ashwin P, Mei Z. (1998) A Numerical bifurcation function for homoclinic orbits,
*SIAM Journal on Numerical Analysis*, volume 35, no. 5, pages 2055-2069, DOI:10.1137/S0036142996298168. - Ashwin P, Terry JR, Thornburg KS, Roy R. (1998) Blowout bifurcation in a system of coupled chaotic lasers,
*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, volume 58, no. 6, pages 7186-7189, DOI:10.1103/PhysRevE.58.7186. - Ashwin P. (1998) Boundary of Two Frequency Behaviour in a System of Three Weakly Coupled Electronic Oscillators,
*Chaos, Solitons and Fractals*, volume 9, no. 8, pages 1279-1287, DOI:10.1016/S0960-0779(98)80001-5. - Ashwin P, Aston PJ. (1998) Blowout bifurcations of codimension two,
*Physics Letters, Section A: General, Atomic and Solid State Physics*, volume 244, no. 4, pages 261-270, DOI:10.1016/S0375-9601(98)00334-X. - Ashwin P, Rucklidge AM. (1998) Cycling chaos: its creation, persistence and loss of stability in a model of nonlinear magnetoconvection,
*PHYSICA D*, volume 122, no. 1-4, pages 134-154, DOI:10.1016/S0167-2789(98)00174-2. [PDF] - Ashwin P, Aston PJ, Nicol M. (1998) On the unfolding of a blowout bifurcation,
*Physica D: Nonlinear Phenomena*, volume 111, no. 1-4, pages 81-95, DOI:10.1016/S0167-2789(97)80006-1. - Ashwin P, Chossat P. (1998) Attractors for Robust Heteroclinic Cycles with Continua of Connections,
*Journal of Nonlinear Science*, volume 8, no. 2, pages 103-129, DOI:10.1007/s003329900045.

### 1997

- Ashwin P, King GP. (1997) A study of particle paths in non-axisymmetric Taylor-Couette flows,
*Journal of Fluid Mechanics*, volume 338, pages 341-362, DOI:10.1017/S0022112097004990. - Ashwin P. (1997) Cycles homoclinic to chaotic sets; robustness and resonance,
*Chaos*, volume 7, no. 2, pages 207-220, DOI:10.1063/1.166221. [PDF] - Ashwin P, Melbourne I. (1997) Noncompact drift for relative equilibria and relative periodic orbits,
*Nonlinearity*, volume 10, no. 3, pages 595-616, DOI:10.1088/0951-7715/10/3/002. - Ashwin P, Tomes J. (1997) Detection of symmetry of attractors from observations II. An experiment with S
4 symmetry,*Physica D: Nonlinear Phenomena*, volume 100, no. 1-2, pages 71-84, DOI:10.1016/S0167-2789(96)00176-5. - Ashwin P, Stone E. (1997) Influence of noise near blowout bifurcation,
*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, volume 56, no. 2, pages 1635-1641, DOI:10.1103/PhysRevE.56.1635. - Ashwin P, Nicol M. (1997) Detection of symmetry of attractors from observations I. Theory,
*Physica D: Nonlinear Phenomena*, volume 100, no. 1-2, pages 58-70, DOI:10.1016/S0167-2789(96)00175-3. - Ashwin P, Chambers W, Petkov G. (1997) Lossless digital filter overflow oscillations; approximation of invariant fractals,
*International Journal of Bifurcation and Chaos in Applied Sciences and Engineering*, volume 7, no. 11, pages 2603-2610, DOI:10.1142/S021812749700176X. - Ashwin P. (1997) Elliptic behaviour in the sawtooth standard map,
*Physics Letters, Section A: General, Atomic and Solid State Physics*, volume 232, no. 6, pages 409-416, DOI:10.1016/S0375-9601(97)00455-6. - Covas E, Ashwin P, Tavakol R. (1997) Non-normal parameter blowout bifurcation: An example in a truncated mean-field dynamo model,
*PHYSICAL REVIEW E*, volume 56, no. 6, pages 6451-6458, DOI:10.1103/PhysRevE.56.6451. [PDF]

### 1996

- Ashwin P, Buescu J, Stewart I. (1996) From attractor to chaotic saddle: A tale of transverse instability,
*Nonlinearity*, volume 9, no. 3, pages 703-737, DOI:10.1088/0951-7715/9/3/006. - Ashwin P, Böhmer K, Mei Z. (1996) Forced symmetry breaking of homoclinic cycles in a PDE with O(2) symmetry,
*Journal of Computational and Applied Mathematics*, volume 70, no. 2, pages 297-310, DOI:10.1016/0377-0427(95)00212-X. - Aronson DG, Krupa M, Ashwin P. (1996) Semirotors in the Josephson Junction Equations,
*Journal of Nonlinear Science*, volume 6, no. 1, pages 85-103, DOI:10.1007/BF02433811.

### 1995

- Ashwin P, Böhmer K, Zhen M. (1995) A numerical liapunov-schmidt method with applications to hopf bifurcation on a square,
*Mathematics of Computation*, volume 64, no. 210, pages 649-670, DOI:10.1090/S0025-5718-1995-1284661-X. - Ashwin P. (1995) Weak coupling of strongly nonlinear, weakly dissipative identical oscillators,
*DYNAMICS AND STABILITY OF SYSTEMS*, volume 10, no. 3, pages 203-218. [PDF] - Ashwin P, Meii Z. (1995) Normal form for hopf bifurcation of partial differential equations on the square,
*Nonlinearity*, volume 8, no. 5, pages 715-734, DOI:10.1088/0951-7715/8/5/004. - Ashwin P, King GP. (1995) Streamline topology in eccentric Taylor vortex flow,
*Journal of Fluid Mechanics*, volume 285, pages 215-247, DOI:10.1017/S0022112095000528. - ASHWIN P, BOHMER K, ZHEN M. (1995) A NUMERICAL LIAPUNOV-SCHMIDT METHOD WITH APPLICATIONS TO HOPF-BIFURCATION ON A SQUARE,
*MATHEMATICS OF COMPUTATION*, volume 64, no. 210, pages 649-&, DOI:10.2307/2153444. [PDF] - ASHWIN P, CHOSSAT P, STEWART I. (1995) TRANSITIVITY OF ORBITS OF MAPS SYMMETRICAL UNDER COMPACT LIE-GROUPS (VOL 4, PG 621, 1994),
*CHAOS SOLITONS & FRACTALS*, volume 5, no. 1, pages 131-131. [PDF] - Ashwin P, Mann GW, King GP. (1995) Azimuthally propagating ring vortices in a model for nonaxisymmetric Taylor vortex flow,
*Phys Rev Lett*, volume 75, no. 25, pages 4610-4613, DOI:10.1103/PhysRevLett.75.4610. [PDF] - Ashwin P. (1995) Attractors stuck on to invariant subspaces,
*Physics Letters A*, volume 209, no. 5-6, pages 338-344, DOI:10.1016/0375-9601(95)00857-8. - Ashwin P, Moroz I, Roberts M. (1995) Bifurcations of stationary, standing and travelling waves in triply diffusive convection,
*Physica D: Nonlinear Phenomena*, volume 81, no. 4, pages 374-397, DOI:10.1016/0167-2789(94)00208-8. - ASHWIN P, SWIFT JW. (1995) TORUS DOUBLING IN 4 WEAKLY COUPLED OSCILLATORS,
*INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS*, volume 5, no. 1, pages 231-241, DOI:10.1142/S021812749500017X. [PDF]

### 1994

- Ashwin P, Zhen M. (1994) A Hopf bifurcation with Robin boundary conditions,
*Journal of Dynamics and Differential Equations*, volume 6, no. 3, pages 487-505, DOI:10.1007/BF02218859. - Ashwin P, Buescu J, Stewart I. (1994) Bubbling of attractors and synchronisation of chaotic oscillators,
*Physics Letters A*, volume 193, no. 2, pages 126-139, DOI:10.1016/0375-9601(94)90947-4. - ASHWIN P, STORK P. (1994) PERMISSIBLE SYMMETRIES OF COUPLED CELL NETWORKS,
*MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY*, volume 116, pages 27-36, DOI:10.1017/S0305004100072364. [PDF] - Ashwin P, Swift JW. (1994) Measuring rotation sets of coupled oscillators,
*Nonlinearity*, volume 7, no. 3, pages 925-942, DOI:10.1088/0951-7715/7/3/009. - Ashwin P, Melbourne I. (1994) Symmetry groups of attractors,
*Archive for Rational Mechanics and Analysis*, volume 126, no. 1, pages 59-78, DOI:10.1007/BF00375696. - Ashwin P, Chossat P, Stewart I. (1994) Transitivity of orbits of maps symmetric under compact lie groups,
*Chaos, Solitons and Fractals*, volume 4, no. 5, pages 621-634, DOI:10.1016/0960-0779(94)90071-X. - ASHWIN P, DANGELMAYR G, STEWART I, WEGELIN M. (1994) OSCILLATOR NETWORKS WITH THE SYMMETRY OF THE UNIT QUATERNION GROUP,
*DYNAMICS, BIFURCATION AND SYMMETRY*, volume 437, pages 35-48. [PDF]

### 1993

- Ashwin P, Swift JW. (1993) Unfolding the torus: Oscillator geometry from time delays,
*Journal of Nonlinear Science*, volume 3, no. 1, pages 459-475, DOI:10.1007/BF02429874. - Ashwin P, Guaschi J, Phelps JM. (1993) Rotation sets and phase-locking in an electronic three oscillator system,
*Physica D: Nonlinear Phenomena*, volume 66, no. 3-4, pages 392-411, DOI:10.1016/0167-2789(93)90075-C.

### 1992

- Ashwin P. (1992) Identical Oscillator Networks with Symmetry,
*Coupled Oscillating Neurons*, Springer Nature, 21-40, DOI:10.1007/978-1-4471-1965-4_2. - Ashwin P, Swift JW. (1992) The dynamics of n weakly coupled identical oscillators,
*Journal of Nonlinear Science*, volume 2, no. 1, pages 69-108, DOI:10.1007/BF02429852. - ASHWIN P. (1992) HIGH CORANK STEADY-STATE MODE INTERACTIONS ON A RECTANGLE,
*BIFURCATION AND SYMMETRY*, volume 104, pages 23-33. [PDF]

### 1990

- Ashwin P, King GP, Swift JW. (1990) Three identical oscillators with symmetric coupling,
*Nonlinearity*, volume 3, no. 3, pages 585-601, DOI:10.1088/0951-7715/3/3/003. - Ashwin P. (1990) Symmetric chaos in systems of three and four forced oscillators,
*Nonlinearity*, volume 3, no. 3, pages 603-617, DOI:10.1088/0951-7715/3/3/004.

## Further information

### Personal Homepage

- Research Interests
- PhD and final year projects
- Centre for Systems, Dynamics and Control at Exeter
- Centre for Systems, Dynamics and Control blog
- MAGIC

- CriticalEarth: Marie Curie ITN training network (EU funded, 2021-2025)
- EPSRC Hub for Qualitative Modelling in Healthcare (EPSRC funded, 2021-2024)
- Applied Nonautonomous Dynamical Systems: Theory, Methods and Examples (EPSRC funded, 2020-2023)
- TiPES: Tipping Points in the Earth System (EU funded, 2019-2023)
- Centre for Predictive Modelling in Healthcare (EPSRC funded, 2015-2020)
- CRITICS ITN (EU funded, 2015-2019)
- CliMathNet (EPSRC funded, 2013-2016)
- ReCoVER (EPSRC funded, 2015-2018)
- European Dynamics Days
- Mathematical Neuroscience Network

- Chaos: An Interdisciplinary Journal of Nonlinear Science (published by AIP)
- Dynamical Systems: an International Journal (published by Taylor and Francis)
- Mathematical Neuroscience and Applications (published by episciences)
- UK-Nonlinear News
- CliMathNet newsletter

- Ruth Chapman
- Saleh Alharthi
- Mohamed Fadera
- Raphael Roemer
- Said Amhemed Elahjel

- Julian Newman
- Nicolas Verscheuren van Rees

- John Terry
- Xin-Chu Fu
- Jon Borresen
- David Hawker
- Marcello Trovati
- Abul Kalam Al-Azad
- John Wordsworth
- Ozkan Karabacak
- Congping Lin
- Jorge Vazquez Diosdado
- Asma Ismail
- Ummu Atiqah Mohd Roslan
- Mary Thoubaan
- Damian Smug
- Hassan Alkhayuon
- Saad Almuaddi
- Jordan Moore
- Ibrahim Alraddadi
- Thoraya Alharthi

- Xin-Chu Fu
- Rob Sturman
- Gabor Orosz
- Konstantin Blyuss
- Prasad Patnaik Behara
- Chris Bick
- Congping Lin
- Jen Creaser
- Camille Poignard
- Tanja Zerenner
- Lea Oljaca

- Dynamics Days Europe, Exeter, Sept 2015
- Workshop on heteroclinic behaviour, 27th March 2012
- Workshop on oscillation dynamics in neural and biochemical systems, 30th Sept 2010
- Workshop on Network Dynamics 15th July 2009
- Workshop on Global Dynamics and Applications, 15-16th June 2009
- Nonlinear Neurodynamics Meeting, 18-19 Sept 2008
- Low complexity Dynamics Meeting, BIRS, Banff, Canada, May 2008
- Nonlinear Neurodynamics Meeting, 5-6 July 2007

### PhD/Masters projects

If you are interested in a PhD or M-level (Math, MSci, MSc) project supervised by myself, it is best to email me for a chat. Below are a list of some topics or areas where I could offer projects. Do also have a look at my publications to see other possible topics that may not be listed below.

**Synchronization and pattern formation in chaotic systems (PhD/M-level)**

The brain is composed of a many neurons each of which has comparatively simple dynamics. One of the fundamental problems in neurophysiology is to understand how such a system can organise itself to permit information processing and storage. This project aims to look at very simple models of such coupled systems in an attempt to understand and classify the possible types of behaviour of such systems, with a view to applying them to more physically relevant models studied by researchers in neurophysiology and physics.

**Spatio-temporal chaos (PhD/M-level)**

We normally think of waves as patterns that propagate in space. Spiral waves are such waves where one end of the wave is pinned at a `spiral core' and the wave rotates around this. Such waves have been observed to arise in many systems, from the behaviour of heart muscle during heart attacks to the oxidation of carbon monoxide on catalytic converters. This project will aim to develop a better understanding of the existence, stability and bifurcation of such waves through the use of dynamical system theory and symmetries.

**Nonlinear dynamics of climate models (PhD/M-level)**

Climate systems or subsystems are often highly nonlinear with a range of feedbacks present. This project will look at some aspects of these models, ranging from "tipping points" to coupled global circulation models.

**Numerical approximation of random attractors (PhD/M-level)**

If a system is forced by a random noise input, one might think that only statistical models will be useful. By viewing the noise as coming from a deterministic dynamical system we can apply a variety of techniques of `random dynamical systems'. This project will examine the existence of and aim to develop new theory for the behaviour of so-called random attractors in numerical approximations of randomly forced system.

**Dynamics in the presence of discontinuities (PhD/M-level) **

The dynamics of systems where all are equations are smooth is at a high level of sophistication. By contrast, those of systems with discontinuities are poorly understood, partly because there are many ways in which this can happen. However there are very basic problems that remain unsolved, for example: consider a triangle in which we play `billiard', i.e. we draw a line inside the triangle and reflect at each boundary it hits. It is unknown whether all triangles have a periodic trajectory, i.e. a trajectory that repeats exactly! Similar problems arise in the mechanics of impacting systems and digital signal processing. There is plenty of scope in this project to specialise on applications or to work on theoretical problems. This project will work with the supervisor and interact with colleagues in Exeter, San Francisco and Marseille at developing a theory for understanding such maps.

**Perceptual rivalry (PhD/M-level) **

For experiments where people are shown differing images appear in each eye, the brain attempts to make sense of the contradictory information by alternating perception between the two different images rather than necessarily trying to fuse them. This is a simple test system where one can begin to understand decision making processes within the brain and there are a variety of mathematical models available to explain the cognitive processes involved. This project will look at some mathematical models of processes including multi-state perceptual rivalry.

**Chaotic attractors and riddled basins (PhD/M-level)**

It is well known that nonlinear iterated mappings can behave in a seemingly unpredictable way; the phenomenon of chao attractors. Basins of attraction for chaotic attractors can display fascinating and complicated fractal geometry, including what has been called riddled basins. This project aims to look at some of the theory and numerical examples of riddled basin attractors.

**Bifurcation theory for differential equations (PhD/M-level) **

Bifurcation theory is a powerful theory for understanding the behaviour of systems of nonlinear differential equations on varying a parameter. By studying the change in solutions one can better understand fundamental instabilities in many systems, focussing on problems in coupled networks of nonlinear dynamical systems.

**Billiards in polygons (PhD/M-level) **

We investigate the mathematics of idealized billiards within a polygon. This is a simple model for a one-particle gas in two dimensions where a particle travels in straight lines between bouncing off the walls. The dynamics of the billiard system depends critically on the shape of the polygon and can be surprisingly non-trivial.

**Fractal dimension and measure (M-level) **

The images of fractals (sets with dimension that is not an integer) are used often in popular culture and for example advertisements; they also have serious uses in science and technology. In fact there are many different types of fractal set that can be characterised in many different ways. This project examines some definitions and fundamentals underlying fractal geometry and dimension before moving on to generate and analyse examples of fractals.

**Evolutionary Game Theory (M-level) **

This project will look at the fundamentals and some applications of evolutionary game theory. This has arisen from applications in biology and economics where interactions between different species or agents lead to them changing their strategy according to a number of models. This project will look in particular at the `replicator equations' and issues of whether a strategy will disappear as a result of the evolutionary game.

**Topics in the History of Mathematics (M-level) **

A possible topic would be a biography of a mathematician or group of mathematicians, or the development of a particular concept or method within mathematics. You will be expected to read original (primary) and secondary sources related to the topic.

### Personal Tutorial Booking

You can book a personal tutorial meeting with me via this link.