报告题目: Spatiotemporal dynamics in the single population model with memory-based diffusion and nonlocal effect

报告人: 宋永利（杭州师范大学教授）

报告时间：2019年9月16日（周一）15:00-16:00

报告地点：文理楼254

报告人简介: 杭州师范大学教授、博士生导师、浙江省高等学校“钱江学者”特聘教授。曾出访西班牙、澳大利亚、加拿大、美国做博士后或合作研究。已在SIAM J. Applied Dynamical Systems, Journal of Differential Equations,  Journal of Nonlinear Science、Nonlinearity、 IEEE Transactions on Neural Networks and Learning Systems、Physica D等国际学术期刊发表学术论文70余篇。2014年起连续5年入选中国高被引学者榜单(数学类)。曾主持、或作为项目组主要成员参与国家自然科学基金重点项目、面上项目、上海市自然科学基金、浙江省自然科学基金等项目十余项。2011年入选教育部新世纪优秀人才计划。2017年获威海市科学技术一等奖（3/3）。2018年入选浙江省151人才工程第一层次培养人选。

报告摘要：

 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 steady state 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. This novel algorithm can be widely used to classify the spatiotemporal dynamics near the Turing-Hopf bifurcation point. Finally, we apply the obtained results to a model proposed by Brit-ton and numerically illustrate the spatiotemporal patterns induced by Hopf, Turing-Hopf and double Hopf bifurcations.

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