Spatiotemporal dynamics in single population model with memory-based diffusion and nonlocal effect

主讲人：宋永利   杭州师范大学教授、博导

时间：2018年12月25日13:30

地点：徐汇校区3号楼332室

举办单位：数理学院

内容简介：

To incorporate spatial memory and nonlocal effect of animal movements, we propose and investigate the spatiotemporal dynamics of the single population model with memory-based diffusion and nonlocal reaction. We first study the stability of a positive equilibrium and the Turing bifurcation induced by diffusion and nonlocality. We then investigate the impact of the averaged memory period on stability and bifurcation, and show that the combination of the averaged memory period and the diffusion can lead to the occurrence of Turing-Hopf and double Hopf bifurcations. The paper originally derives the normal form theory for Turing-Hopf bifurcation in the general reaction-diffusion equation with memory-based diffusion and nonlocal reaction. Finally, we apply the obtained results to a model proposed by Britton and numerically illustrate the spatialtemporal patterns induced by Hopf, Turing-Hopf and double Hopf bifurcations.