Speaker: Oliver Steinbock
Abstract. Excitable systems are ubiquitous in nature. Prominent examples include neuronal and cardiac tissue, catalytic surface reactions and spreading diseases. These systems have traveling wave solutions (e.g. the "Mexican wave" in football stadia) which organize rotating spirals in two-dimensional media and rotating scroll waves in 3D. Chemical reaction-diffusion systems provide convenient models to systematical study the dynamics of these vortex patterns. In my talk, I will review the underlying nonlinear rate laws of these chemical systems, explain tomographic reconstruction techniques, and discuss scroll wave solutions, their dynamics, phase evolution and instabilities. Our findings link these aspects directly to spatio-temporal chaos, curvature flow problems and the nonlinear Burgers equation.