Spatial and temporal periodic patterns in a delayed diffusive plant–pollinator model with memory-based diffusion

Abstract

In this paper, incorporating memory-based diffusion and delay, we propose a partly diffusive plant–pollinator model under Neumann boundary condition. Then, we investigate the effects of memory-based diffusion and delay on the dynamics of this model through discussing the corresponding characteristic equation. And we find that Turing bifurcations and Hopf bifurcations can be induced by memory-based diffusion and delay, respectively. By performing some numerical simulations, stable spatially homogeneous periodic solutions and inhomogeneous steady state solutions are obtained, which illustrates and expands our results in this paper. Moreover, the unstable spatially inhomogeneous periodic solutions occur only for some time, then they eventually converge to a spatially homogeneous periodic solutions.