“数理论坛”第133期：Global dynamics and spatio-temporal dynamics of Predator-prey systems with density-dependent motion

报告题目

Global dynamics and spatio-temporal dynamics of Predator-prey systems with density-dependent motion

报告时间

2019年12月16日（周一）15:30—17:00

报告地点

东区教学科研综合楼A1404会议室

报告人

王治安（香港理工大学应用数学系）

报告人

简介

王治安，香港理工大学应用数学系教授

报告摘要

In this talk, we discuss the global boundedness, asymptotic stabilityand pattern formation of predator-prey systems with density-dependent prey-taxisin a two-dimensional bounded domain with Neumann boundary conditions, where thecoefficients of motility (diffusion) and mobility (prey-taxis) of the predator are correlatedthrough a prey density dependent motility function. We establish the existence ofclassical solutions with uniform-in time bound and the global stability of the spatiallyhomogeneous prey-only steady states and coexistence steady states under certain conditionson parameters by constructing Lyapunovfunctionals. With numerical simulations,we further demonstrate that spatially homogeneous time-periodic patterns, stationaryspatially inhomogeneous patterns and chaotic spatio-temporal patterns are all possiblefor the parameters outside the stability regime. We also find from numerical simulationsthat the temporal dynamics between linearized system and nonlinear systems are quitedifferent, and the prey density-dependent motility function can trigger the pattern formation.

邀请人

郭上江 教授

2019年12月15日