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Research interests

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:

Dr Ozgur Akman Network modelling in biological systems
Professor Peter Ashwin Coupled dynamics, critical transitions, tipping points, applications
Professor Vadim N Biktashev Excitable systems, autowaves
Dr Marc Goodfellow Complex networks, intermittency
Dr Frank Kwasniok Data-driven and statistical methods, especially in climate and weather science
Dr Prathyush P Menon Control theory, aerospace guidance systems, space applications
Dr Jan Sieber Critical transitions, network dynamics
Professor Krasimira Tsaneva-Atanasova Spatially extended dynamics, hybrid systems

Academic staff associated with the centre with research interests in this area include

For more information, contact Professor Krasimira Tsaneva-Atanasova or Professor Peter Ashwin.

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.

Academic staff in mathematics with research interests in this area include:

Dr Demi Allen Fractal geometry, metric diophantine approximation, shrinking target problems
Professor Peter Ashwin Bifurcation theory and ergodic approaches to chaotic systems, symmetry
Professor Vadim N Biktashev Singular perturbation theory for PDEs and dynamical systems
Professor Mark Holland Statistical properties of chaotic attractors, extremes
Dr Ana Rodrigues Low-dimensional dynamics, ergodic theory, systems with symmetry
Professor Jan Sieber Bifurcation theory, continuation, delay differential equations

For more information, contact Professor Peter Ashwin.

Dynamics of Living Systems

With the founding of the Living Systems Institute, Exeter mathematics has expanded its research into interdisciplinary approaches to understand living systems and disease. Our group provides underpinning research for the Living Systems Mathematics group and the EPSRC Centre for Predictive Modelling in Healthcare. We focus on applications of nonlinear dynamical systems and complex networks theory to a variety of living systems. Specific areas of active research in the centre include the folllowing:

Mathematical neuroscience, Mathematical endocrinology, Computational biology (from subcellular to whole systems), Biological pattern formation, Circadian and ultradian rhythms, Cardiac modelling.

Academic staff in mathematics with research interests in this area include

Professor Peter Ashwin Cell transport processes, mathematical neuroscience
Professor Vadim N Biktashev Pattern formation, cardiac modelling, mathematical ecology
Dr Christian Bick Dynamics of networks, neuroscience

Beatbox

Professor 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).