報告題目：Effect of nonlocality on the dynamics of memory-based diffusion equations
報告人：宋永利 教授 （杭州師範大學數學必一）
報告時間：2023年5月18日（星期四）下午14:30-15:30
報告地點：卓越樓425
報告摘要： 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.
宋永利教授簡介: 杭州師範大學教授、博士生導師、浙江省高等學校“錢江學者”特聘教授、中國生物數學會理事。曾出訪西班牙、澳大利亞、加拿大、美國做博士後或合作研究。主要從事微分方程定性理論、無窮維動力系統的分支理論、斑圖動力學的研究工作，取得了一系列高水平的研究成果，在動力系統領域的國際權威期刊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等雜誌發表SCI論文80余篇,被國內外同行引用2000余次。2014年起連續入選中國高被引學者榜單（數學類）。 曾主持多項國家自然基金和省部級基金項目的研究工作。2011年入選教育部新世紀優秀人才、2018年入選浙江省151人才工程第一層次培養人選、2020年榮獲杭州市優秀教師稱號。研究成果獲威海市科學技術一等獎（3/3）和浙江省自然科學三等獎（1/4）。