Nonlinear Dynamics and Pattern Formation

Understanding the spontaneous formation and dynamics of spatio-temporal patterns in dissipative non-equilibrium systems is one of the major challenges in nonlinear sciences. We study the emergence of macroscopic spatio-temporal order due to self-organization in complex physical, biological and chemical systems far from thermodynamic equilibrium. Systems under consideration represent cooperative fields of a large number of spatially interacting subunits with bistable, excitable or oscillatory nonlinear dynamics. The entire system is capable of showing a variety of pattern formation and unexpected behaviour impossible under equilibrium conditions. Although our work is interdisciplinary basic research there is a variety of possible future applications in medicine, chemical engineering, and many other areas.

In more detail our focus is on:

1. Theory of propagation, stability and interaction of wave-like nonlinear excitations (fronts, pulses, periodic pulse trains, spiral waves) that are of fundamental importance for the understanding of communication inside and between cells, for example.
2. Control of spiral wave dynamics by feedback-mediated parameter modulation. This is important for the therapy of abnormal electrical wave activity in the heart (tachycardia) or the brain (epilepsy, migraine).
3. Instabilities in media with long-range spatial coupling (global and non-local) arising quite naturally in neural networks, catalytic surface reactions, electrochemical systems and others.
4. Noise-induced pattern formation, stochastic theory of nonlinear processes in spatially extended media with fluctuating parameters.
5. Theoretical and experimental studies of chemical waves (in photosensitive Belousov-Zhabotinsky medium).