Dynamical Systems and Analysis
Dynamical Systems and Analysis
Members of the Dynamical Systems & Analysis group work on dynamical systems theory, probability and their applications in life and physical sciences. Our research is divided into three overlapping themes: Analysis of Dynamical Systems, Applications of Dynamical Systems and Complexity and Control. Further information about our multidsiciplinary work can be found on the Centre for Systems, Dynamics and Control website.
Our seminars are listed here.
Research interests
Our group works on mathematical theory underpinning application areas. Our theoretical research involves for example
- recurrence properties of one dimensional maps and coupled differential equations,
- dynamical networks, their symmetries and control,
- nonautonomous and random dynamical systems,
- probabilistic approaches to dynamical systems,
- pattern formation in spatially extended systems
As a common theme we use advanced mathematical methodologies to understand, predict and control the dynamical behaviour of complex nonlinear systems. Our main application areas:
- Living systems and Healthcare modelling
- Dynamical systems theory studying, eg, tipping and extreme events in climate
- Complexity and control of networks
Find out more about these main application areas by clicking on the tabs below:
Analysis of Dynamical Systems
The mathematical theory of dynamical systems is mature and vital part of modern mathematics, where new theoretical developments have been inspired by applications, just as new developments in pure mathematics have quickly found dynamical applications. Because of this, this area forms a strong bridge between pure and applied mathematics. Research undertaken at the centre is at the forefront of developing and applying new mathematical results in a range of applications. Specific areas of active research in the centre include:
Chaotic and deterministic behaviour, Bifurcation theory, Ergodic theory, Differential equations, Dynamics with symmetries, Applications to number theory and geometry
Academic staff in mathematics with research interests in this area include:
| Demi Allen | Fractal geometry, metric diophantine approximation, shrinking target problems |
| Peter Ashwin | Bifurcation theory and ergodic approaches to chaotic systems, symmetry |
| Vadim N Biktashev | Singular perturbation theory for PDEs and dynamical systems |
| Mark Holland | Statistical properties of chaotic attractors, extremes |
| Ana Rodrigues | Low-dimensional dynamics, ergodic theory, systems with symmetry |
| Jan Sieber | Bifurcation theory, continuation, delay differential equations |
For more information, contact Jan Sieber.
Complexity and Control
For larger complex systems there are great challenges in finding the appropriate mathematical framework to understand and (if possible) control their behaviour. In addition to structural complexity and heterogeneity, many real world system questions require a range of mathematical and computational skills in order to find answers. Specific areas of active research in the centre include the following:
Control theory, Hybrid testing of biological and mechanical systems, Multiscale systems and computational modelling, Complex networks and emergent phenomena, Coupled and delayed dynamical systems, Applications to engineering, physical, earth and life sciences
Academic staff in mathematics with research interests in this area include:
| Peter Ashwin | Coupled dynamics, critical transitions, tipping points, applications |
| Vadim N Biktashev | Excitable systems, autowaves |
| Frank Kwasniok | Data-driven and statistical methods, especially in climate and weather science |
| Jan Sieber | Critical transitions, network dynamics |
Many other staff across the university are active in this area - see the Centre for Systems, Dynamics and Control.
For more information, please contact Peter Ashwin.
Applications of Dynamics
This group is actively involved in a collaborations that apply interdisciplinary approaches to a wide variety of systems in the life, earth and physical science. This includes the Living Systems Institute which uses interdisciplinary approaches to understand living systems and disease. Our group provides underpinning research for and applications of nonlinear dynamical systems and complex networks theory to
Academic staff in mathematics with research interests in this area include
| Peter Ashwin | Applications to cell biology processes, neural networks, climate and earth systems |
| Vadim N Biktashev | Applications to cardiac modelling, mathematical ecology |
| Mark Holland | Applications to extremes in climate and weather |
| Frank Kwasniok | Applications to climate and weather science |
| Jan Sieber | Applciations to continuation in experiments, climate tipping and semiconductor lasers |
Centre for Systems, Dynamics and Control
The Centre for Systems, Dynamics and Control acts as a focus for interdisciplinary work in Dynamical Systems for researchers in the Department and across the University.
Beatbox
Vadim N Biktashev has developed and actively maintains the open-source HPC Environment for Biophysically and Anatomically Realistic Cardiac Simulations BeatBox (development supported by EPSRC EP/I029664/1).
Hub for Quantitative Modelling in Healthcare
Peter Ashwin is an investigator with the EPSRC Hub for Quantitative Modelling in Healthcare (supported by EPSRC EP/T017856/1) which aims to promote quantitative modelling in various aspects of healthcare, especially in neuroscience and endocrine modelling.
