报告题目：Effect of nonlocality on the dynamics of memory-based diffusion equations

报告人：宋永利，杭州师范大学

地点： 数学楼2-3

时间：2023年5月25日16:00- 17：00

报告摘要：In this talk, the influence of the distributed delay (nonlocality in time) and nonlocal delay (nonlocality in space) on the stability and spatiotemporal dynamics in the memory-based diffusion populations are discussed. For the distributed delay, it has been shown that the weak kernel does not affect the stability of this positive constant steady state, but the strong kernel can lead to the rich dynamics. For the nonlocal delay, it has been shown that when movement driven by the memory-based diffusion is slow, the memory does not the  stability of positive homogeneous steady state, but when the movement driven by the memory-based diffusion is fast, the small memory delay (no matter how small it is) can destabilize the stability, however the large memory can stabilize the stability. A series of Turing bifurcation, Hopf bifurcation, Turing-Turing bifurcation and double Hopf bifurcation are explicitly determined.

宋永利教授简介：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、教育部新世纪优秀人才。主要从事微分方程定性理论、无穷维动力系统的分支理论、斑图动力学的研究工作，在动力系统领域的国际权威期刊SIAM Journal on Applied Dynamical System、Nonlinearity、Journal of Nonlinear Science、Journal of Differential Equations、Studies in Applied Mathematics、Journal of Dynamics and Differential Equations、Physica D等杂志发表SCI论文90余篇，连续多年入选中国高被引学者榜单（数学类），2022年入选斯坦福大学发布的全球前2%顶尖科学家榜单。曾主持多项国家自然基金和省部级重点项目的研究工作。2018年入选浙江省151人才工程第一层次培养人选、2020年荣获杭州市优秀教师称号。研究成果获威海市科学技术一等奖和浙江省自然科学三等奖。