One-dimensional reaction-diffusion dynamics in spatially bounded domains

Abstract We consider the complex dynamics arising in a one-dimensional advection-reaction-diffusion system along with its bistable cubic variant. In both cases, we analyze the dynamics in a bounded domain, assuming, first, Robin, and then periodic boundaries. We study the stability of the solutions obtained and suggest eventual implications in the experimental study of chemical waves as well as in a simplified description of cardiac electric signal propagation.