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

發布者:文明辦發布時間:2018-12-21浏覽次數:10


主讲人:宋永利   杭州师范大学教授、博导


時間:2018年12月25日13:30


地點:徐彙校區3號樓332室


舉辦單位:數理學院


內容簡介:

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.