讲座题目：Spatiotemporal dynamics of a diffusive consumer-resource model with explicit spatial memory

主讲人：宋永利教授（杭州师范大学）

讲座时间：2021年11月30日9：00-10：00

讲座地点：腾讯会议（ID: 560-701-038）

理学院

2021年11月29日

摘要：Spatial memory is inevitable in animal movement modeling but elusive in many classical models. A nonlocal integral term involving space is a traditional way to incorporate spatial memory, but the actual spatial memory should depend on past information so that delay naturally arises. We propose a new consumer-resource model with random and memory-based diffusions in

which the resource species has no memory or cognition, whereas the consumer species has spatial memory. By using the memory-based diffusion coefficient and the averaged memory period of the consumer as the control

parameters, we find Hopf bifurcations and stability switches occur and spatially nonhomogeneous periodic solutions are generated. It is well known that prey-taxis enhances the stability of a homogeneous coexistence state in a predator–prey system, and here we show that memory-based prey-taxis can destabilize a constant coexistence and generate complex spatiotemporal pattern formation. Using the obtained theoretical results, we study the impact of the memory-based diffusion on the consumer-resource dynamics with Holling type-I and type-II functional responses.

主讲人简介：

宋永利，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、中国生物数学会理事。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。连续多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。2017年获威海市科学技术一等奖（3/3）、2020年获杭州市优秀教师称号。