讲座题目：Classification of global dynamics of a periodic diffusive consumer-resource model
主讲人：王治安 教授
主持人：叶东 教授
开始时间：2025-6-6 13:30
讲座地址：闵行数统楼北楼401报告厅
主办单位：数学科学学院
报告人简介：
王治安，香港理工大学教授，华中师大本科硕士，加拿大艾伯塔大学应用数学博士，美国明尼苏达大学应用数学所博士后。主要从事与生物数学相关的偏微分方程研究，兴趣包括生物和生态数学中动力学行为与运动的建模与分析。目前担任J. Math. Biol., DCDS-B， Frontiers in Ecology and Evolution杂志编委。多次获得香港研究资助局基金资助和2022国家基金委-香港研究资助局联合研究基金资助，获得过2013 JMAA Ames Award 和2019香港数学会青年学者奖。
报告内容：
We consider a reaction-diffusion model describing the consumer-resource interactions, where the resource's input rate may be temporally periodic and spatially heterogeneous. By employing the parabolic comparison principle, method of super-lower solutions for the mixed-quasilinear monotone system, theory for asymptotically periodic systems, uniform persistence theory for infinite-dimensional dynamical systems, and principal eigenvalue theory, we classify the persistence and extinction dynamics of the consumer population in terms of dispersal rates and relaxation time classified by the mortality rate of the consumer. Furthermore, we derive the asymptotic profiles of positive periodic solutions as the resource's dispersal rate is sufficiently small or large. Our results elucidate how the consumer's mortality rate, the relaxation time, the spatiotemporal heterogeneity of the resource's input, and the dispersal rates affect the global dynamics of consumer and resource populations. In particular, our analytical results derive the following implications: (a) the resource's decay is the dominant factor that can prevent the resource abundance from blowing up; (b) the consumer’s mortality rate is a key factor determining the persistence and extinction for the consumer population; (c) the temporally homogeneous resource input may be more beneficial to the consumer's persistence than the temporally varying input when the consumer’s mortality is moderate.
