Competing spatial and temporal instabilities in a globally coupled bistable semiconductor system near a codimension-two bifurcation

Abstract

We study complex spatiotemporal dynamics in a globally coupled bistable reaction-diffusion model on a two-dimensional spatial domain. It is demonstrated that complex behavior appears near a codimension-two bifurcation point due to the competition of spatial and temporal instabilities. We derive sufficient conditions for the appearance of mixed spatiotemporal modes, and clarify the origin of a menagery of complex dynamics, such as periodic and chaotic oscillations of current filaments, low-dimensional spatiotemporal chaos including a Shil'nikov attractor, and periodic back-and-forth motion of current density fronts. Such dynamics is found in a wide range of domain sizes for square and rectangular domains. The type of dynamics is sensitive to small variations in the domain shape. We discuss and explain the differences between spatiotemporal dynamics on one-dimensional and two-dimensional domains.