Heterogeneity-induced effects for pulse dynamics in FitzHugh-Nagumo-type systems

Particle like structures have been observed in many fields of science. In a homogeneous medium, a stable, standing pulse is a localized wave that may arise when nonlinear and dissipative effects are in balance. In this paper, we investigate certain phenomena associated with the dynamics of pulse solutions for a FitzHugh-Nagumo reaction-diffusion model. When two pulses are located far from one another initially, their weak interaction drives the subsequent slow dynamics. Our comprehension of the standing pulse profiles allows us to quantitatively characterize their interplay; when the diffusivity of the activator is small compared to that of the inhibitor, the two pulses repel. In addition, using a center-manifold reduction to study the presence of heterogeneities in the environment, we demonstrate that the pulses will move so as to maximize the strength of activation or minimize that of inhibition. The pulse motion will also be influenced by the reaction mechanism.