报告题目：Spatiotemporal dynamics induced by nonlocal advection in the reaction-diffusion equation
报告人：宋永利 教授
报告时间：2024年5月19日（星期日）上午9:00-10：00
报告地点：管理学院第二会议室
报告摘要：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.
报告人简介: 宋永利，杭州师范大学数学学院教授、博士生导师、教育部新世纪优秀人才、浙江省高等学校“钱江学者”特聘教授、中国生物数学会理事。 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 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等发表学术论文90余篇。2014年起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年获“杭州市优秀教师”、“浙江省优秀数学教师”和“杭州师范大学优秀研究生导师”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。