报告题目：Effect of nonlocality on the dynamics of memory-based diffusion equations
报告人：宋永利 教授 （杭州师范大学数学学院）
报告时间：2023年5月18日（星期四）下午14:30-15:30
报告地点：卓越楼425
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、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。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，取得了一系列高水平的研究成果，在动力系统领域的国际权威期刊SIAM Journal on Applied Dynamical Systems、Nonlinearity、Journal of Nonlinear Science、Journal of Differential Equations、Studies in Applied Mathematics、Journal of Dynamics and Differential Equations、Physica D、IEEE Transactions on Neural Networks and Learning Systems等杂志发表SCI论文80余篇,被国内外同行引用2000余次。2014年起连续入选中国高被引学者榜单（数学类）。 曾主持多项国家自然基金和省部级基金项目的研究工作。2011年入选教育部新世纪优秀人才、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（3/3）和浙江省自然科学三等奖（1/4）。