Stability and Bifurcation Analysis for a Two-Species Diffusive Model with Memory-Based Diffusion

Spatial memory has important influence on the mechanistic modeling of animal movements. In this paper, we study a model of two interacting species with sensitivity function and spatial memory. We first show the existence and global boundedness of positive solutions. We explore the influence of the sensitivity function on the stability and Turing bifurcation. Then the joint effect of the sensitivity function and the memory delay on the stability and spatio-temporal dynamics is investigated. We find that the high sensitivity of spatial memory is easier to induce Hopf bifurcation, generating spatially inhomogeneous periodic solutions, which is a new mechanism to induce Hopf bifurcation. Finally, the normal form of Hopf bifurcation is also derived.