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数学与信息科学学院反应扩散方程系列报告

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报告人:金瑜副教授、何小清教授

讲座日期:2020-06-22

讲座时间:08:30

报告地点:腾讯会议(ID:319 823 513

主办单位:数学与信息科学学院

讲座题目1The dynamics of a zooplankton–fish system in aquatic habitats

报告人:金瑜 副教授

讲座时间:08:30

讲座内容简介:

Diel vertical migration is a common movement pattern of zooplankton in marine and freshwater habitats. In this work, we use a temporally periodic reaction–diffusion–advection system to describe the dynamics of zooplankton and fish in aquatic habitats. Zooplankton live in both the surface water and the deep water, while fish only live in the surface water. Zooplankton undertake diel vertical migration to avoid predation by fish during the day and to consume sufficient food in the surface water during the night. We establish the persistence theory for both species as well as the existence of a time-periodic positive solution to investigate how zooplankton manage to maintain a balance with their predators via vertical migration. Numerical simulations discover the effects of migration strategy, advection rates, domain boundary conditions, as well as spatially varying growth rates, on persistence of the system.

讲座人简介:

金瑜,美国内布拉斯加大学林肯分校数学系副教授。2009年于加拿大纽芬兰纪念大学获得博士学位,导师赵晓强教授;2009年至2012年于加拿大阿尔伯塔大学从事博士后工作,导师Mark. A. Lewis教授;2012年至今于美国内布拉斯加大学林肯分校先后任助理教授,副教授。研究领域包含微分方程和动力系统及其在生物种群中的应用。已在SIAM J. Appl. Math.、SIAM J. Math. Anal.、SIAM J. Appl. Dyn. Syst.、J. Math. Biol.、Bull. Math. Biol.、J. Nonlinear Sci.、Am. Nat.、J. Dynam. Differ. Equat.等国际著名SCI杂志上发表学术论文20多篇。

讲座题目2On the effects of carrying capacity and intrinsic growth rate on single and multiple species in spatially heterogeneous environments

报告人:何小清 教授

讲座时间:10:30

讲座内容简介:

We consider a diffusive logistic model of a single species in a heterogeneous environment, with two parameters, r(x) for intrinsic growth rate and K(x) for carrying capacity. When r(x) and K(x) are proportional, i.e., r=cK, it is proved by Prof. Yuan Lou that a population diffusing at any rate will reach a higher total equilibrium biomass than the population in an environment in which the same total resources are distributed homogeneously. This talk considers another case when r(x) is a constant, i.e., independent of K(x). In such case, a striking result is that for any dispersal rate, the logistic equation with spatially heterogeneous resources will always support a total population strictly smaller than the total carrying capacity at equilibrium, which is just opposite to the case r = cK. These two cases of single species models also lead to two different forms of Lotka-Volterra competition-diffusion systems. We then report the consequences of the aforementioned difference on the two forms of competition systems. Our results indicate that in heterogeneous environments, the correlation between r(x) and K(x) has more profound impacts in population ecology then we had previously expected, at least from a mathematical point of view. This is joint work with Qian Guo and Prof. Wei-Ming Ni.

讲座人简介:

何小清教授,2007年在西安交通大学获得学士学位,2013年在明尼苏达大学获得博士学位,导师为倪维明教授。2013年至2015年在台湾理论科学研究中心做博士后。目前为华东师范大学青年研究员,主要研究兴趣包括空间异性的非线性椭圆型和抛物型偏微分方程/方程组,及其在种群生态学中的应用,在CPAM、JDE、CVPDE、JMB等国际数学期刊发表多篇学术论文。

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