Research Interests
Dynamics of complex systems, especially the intermittent dynamics of large networks of coupled dynamical systems.
Bifurcation theory and dynamical systems, especially for synchronisation problems and symmetric chaotic dynamics.
Applications of dynamical and complex systems theory to:
Magnetohydrodynamic flows (bifurcations and mixing)
Laser systems (synchronization)
Electronic systems (digital signal processing)
Climate system and earth sciences (precursors to bifurcations)
Nonlinear models in Neuroscience via collective dynamics of coupled systems and “winnerless competition” models in cognitive processes.
Intermittent behaviour in nonlinear chaotic systems and structure of attractors. Riddled basins of attraction and associated phenomena.
Random dynamics and modelling of stochastically forced systems by determinstic skew product systems.
Topics of study in my research include:
Systems with invariant subspaces where one can find attractors with riddled basins, i.e. an attractor whose basin has full measure but such that basins of other attractors are open and dense in the whole phase space
The dynamical behaviour of skew product and random dynamical systems, and the dynamics of systems with noncompact symmetry groups.
Homoclinic behaviour, especially in systems with symmetries (Click here to see the basin of attraction of a single connections within a continuum of connections forced to exist by symmetry). Homoclinic and heteroclinic orbits to chaotic invariant sets (`cycling chaos').
Lagrangian mixing properties of fluid flows; advection of passive scalars in such flows.
Coupled oscillator dynamics. Many physical systems can be thought of as interacting systems of coupled oscillators. Mathematically one can exploit symmetry to solve many examples of analytically tractable models with interesting dynamics.
Applications of coupled oscillator to neural computing.
Numerical computation of bifurcation behaviour; in particular computation of steady-state, Hopf and homoclinic bifurcations of nonlinear systems.
Discontinuous linear mappings, especially piecewise isometries such as the overflow oscillation problem and the sawtooth standard mapping.
For more details, please email me or have a look at my publication list (many of which are downloadable in preprint form).
I am co-editor (with Matthew Nicol) of the Journal Dynamical Systems. This is a quarterly journal, published by Taylor and Francis . We publish research papers in the area of dynamical systems and applications in any area and welcome the submission of high quality research articles. For more details, see the journal webpage.
Some examples of symmetric chaos in mappings of the plane are here.
Here is an overflow oscillation problem simulator.
You can see the attractors for two coupled logistic maps here.
A simple web-based dynamical systems simulator (with contributions from E Koufopolou and A. Chui) can be found here.
Recent EPSRC funded research:
Project EP/C510771 on the dynamics and control of assemblies of coupled oscillators; investigation of synchronization, adaptation and computational aspects; with Prof S. Townley (Exeter). Final Report
Other collaborations with a range of people including: A. Goetz (San Francisco), M. Field (Houston), I. Melbourne (Surrey), Xinchu Fu (Shanghai), Jonathan Deane (Surrey), E. Covas and R. Tavakol (QMW), G. Dangelmayr (Colorado State), E. Stone (Utah State), Mei Zhen (Marburg), M. Nicol (Surrey), W. Chambers (KCL), P. Chossat (Nice), K Tchizawa (Tokyo), J. Buescu (Porto), R. Roy (Maryland), J. Swift (NAU), O. Podvigina (Moscow), K. Zyczkowski (Warsaw).
Past PhD students:
John R Terry (2000)
Xin-Chu Fu (2002)
Jon Borresen (2005)
David Hawker (2005)
Marcello Trovati (2007)
Current PhD students:
John Wordsworth (2005-)
Abul Kalam Al-Azad (2006-)
Özkan Karabacak (2007-)
Click here if you want to see a list of my publications and preprints
