報告題目：Spatiotemporal dynamics induced by nonlocal advection in the reaction-diffusion equation
報告人：宋永利 教授
報告時間：2024年5月19日（星期日）上午9:00-10：00
報告地點：管必一体育平台第二會議室
報告摘要：We formulate a diffusive consumer-resource model with nonlocal advection on resource availability, where resource dynamics is explicitly modeled, to investigate the influence of nonlocal perception on stability and spatiotemporal patterns. For the finite domain, nonlocal perception described by two common types of resource detection function (spatial average or Green function) has no impact on the stability of the spatially homogeneous steady state. For the infinite domain, nonlocal perception described by the Laplacian or Gaussian detection function has no impact on stability either; however, the top-hat detection function can destabilize the spatially homogeneous steady state when the rate of perceptual movement is large and the detection scale belongs to an appropriate interval. Using the more realistic top-hat perception kernel, we investigate the influence of the detection scale, the perceptual movement rate and the resource’s carrying capacity on the spatiotemporal patterns and find the stripe spatial patterns, oscillatory patterns with different spatial profiles as well as spatiotemporal chaos.
報告人簡介: 宋永利，杭州師範大學數學必一教授、博士生導師、教育部新世紀優秀人才、浙江省高等學校“錢江學者”特聘教授、中國生物數學會理事。 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 J. Applied Dynamical Systems、 Journal of Differential Equations、 Journal of Nonlinear Science、Nonlinearity、Studies in Applied Mathematics、 IEEE Transactions on Neural Networks and Learning Systems、Physica D等發表學術論文90余篇。2014年起連續多年入選中國高被引學者榜單(數學類)。 2022年入選斯坦福大學發布的全球前2%頂尖科學家榜單。曾主持多項國家自然基金和省部級重點項目的研究工作。2018年入選浙江省151人才工程第一層次培養人選、 2020年獲“杭州市優秀教師”、“浙江省優秀數學教師”和“杭州師範大學優秀研究生導師”稱號。研究成果獲威海市科學技術一等獎和浙江省自然科學三等獎。