Stability and spatiotemporal patterns of a memory-based diffusion equation with nonlocal interaction

Abstract

In this paper, we investigate the spatiotemporal dynamics driven by the memory delay and nonlocal interaction for the memory-based diffusion equation, where the nonlocal interaction is characterized by the given Green function. It has been shown that this kind of nonlocal interaction can lead to inhomogeneous steady states with any modes, and the joint effect of nonlocal interaction and memory delay can lead spatially inhomogeneous Hopf bifurcation and Turing–Hopf bifurcation.