Title:

Dynamics of fronts in a multi-component reaction-diffusion system: when Takens-Bogdanov meets a butterfly catastrophe

Abstract:

Understanding the formation of patterns is of interest in various fields of science and, hence, a much studied subject in applied analysis. In order to rigorously study the evolution of patterns such as stripes or spots, it is crucial to first analyze single interfaces, that is, front solutions. Along the example of a multicomponent reaction-diffusion system, we demonstrate that even single front solutions can exhibit surprisingly rich dynamics. To this end, we use center manifold reduction in infinite dimensions and study the resulting reduced system that describes the temporal evolution of the front velocity. We close the exposition by anticipating the implications of our analysis for patterns in 2D.