Global dynamics of a Lotka-Volterra competition-diffusion system in advective homogeneous environments

发布时间:2023年05月21日 作者:戴斌祥   阅读次数:[]

报告题目:Global dynamics of a Lotka-Volterra competition-diffusion system in advective homogeneous environments

报告时间:2023525 (星期四) 上午09:00-11:00

报告地点:线下:数学院467办公室; 线上:腾讯会议--263-288-928

报告人:Yuming  Chen(陈玉明) 教授 (Wilfrid Laurier University)

报告摘要:In this joint work with Dr. De Tang, we mainly study a two-species competition model in a one-dimensional advective homogeneous environment, where the two species are identical except their diffusion rates. One interesting feature of the model is that the boundary condition at the downstream end represents a net loss of individuals, which is tuned by a parameter $b$ to measure the magnitude of the loss. When the upstream end has the no-flux condition, Lou and Zhou (Y. Lou and P. Zhou, Evolution of dispersal in advective homogeneous environment: The effect of boundary conditions, J. Differential Equations, 259 (2015) 141-171) have confirmed that large diffusion rate always wins when $0<b<1$. Here we consider the case where the upstream end has the flow-free condition, which means that the upstream end is linked to a lake. We firstly investigate the corresponding single species model. With a new approach, we establish the existence and uniqueness of positive steady states. Then for the two-species model, we find that the parameter $b$ can be regard as a bifurcation parameter. Precisely, when $0\leq b<1$, large diffusion rate always wins while when $b>1$, small diffusion rate is selected. When $b=1$, there is a compact global attractor and it consists of a continuum of steady states $\{(l,(r-l)): l\in[0,r]\}$ connecting the two semi-trivial steady states, where $r$ is the intrinsic growth rate for both species.

报告人简介:Yuming Chen(陈玉明),加拿大罗瑞尔大学(Wilfrid Laurier University)教授。2000年从加拿大约克大学(York University)获理学博士学位,随后在加拿大阿尔伯塔大学(University of Alberta)做博士后。自20017月起,一直任教于加拿大罗瑞尔大学,现为该校数学系终身教授。主要研究兴趣为动力系统和泛函微分方程理论及其在生物数学和神经网络中的应用,在SIAM Journal on Mathematical Analysis, Nonlinearity, Journal of Differential Equations, Physica D, Proceedings of the American Mathematical Society, Mathematical Biosciences, Neural Networks等国际著名刊物发表论文近百篇。曾获安大略省科技与创新部早期研究者奖。主持了4项加拿大国家自然科学与工程理事会(NSERC)科研基金项目,参与了3项中国国家自然科学基金面上项目。

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