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​理学院迎百年校庆系列报告十八——Persistence and extinction dynamics in reaction-diffusion-advection stream population model with Allee effect growth
发布单位:理学院        浏览次数:12        发布时间:2019年10月06日

    应理学院数学系邀请,北京师范大学博士后王妍将于20191007日访问我校数学系,期间将作学术报告,欢迎感兴趣的师生参加。 

报告时间:20191007日(周一)下午300 - 400 

报告地点:H203 

报告题目Persistence and extinction dynamics in reaction-diffusion-advection stream population model with Allee effect growth

AbstractThe question how aquatic populations persist in rivers when individuals are constantly lost due to downstream drift has been termed the “drift paradox”. Reaction-diffusion-advection models have been used to describe the spatial-temporal dynamics of stream population and they provide some qualitative explanations to the paradox. In this work, the effect of spatially varying Allee effect growth rate on the dynamics of reaction-diffusion-advection models for the stream population is studied.

First, a reaction-diffusion-advection equation with strong Allee effect growth rate is proposed to model a single species stream population in a unidirectional flow. Under biologically reasonable boundary conditions, the existence of multiple positive steady states is shown when both the diffusion coefficient and the advection rate are small, which lead to different asymptotic behavior for different initial conditions. On the other hand, when the advection rate is large, the population becomes extinct regardless of initial condition under most boundary conditions. It is shown that the population persistence or extinction depends on Allee threshold, advection rate, diffusion coefficient and initial conditions, and there is also rich transient dynamical behavior before the eventual population persistence or extinction.

Then followed the dynamical behavior of a reaction-diffusion-advection model of a stream population with weak Allee effect type growth. Under the open environment, it is shown that the persistence or extinction of population depends on the diffusion coefficient, advection rate and type of boundary condition, and the existence of multiple positive steady states is proved for intermediate advection rate using bifurcation theory. On the other hand, for closed environment, the stream population always persists for all diffusion coefficients and advection rates.

In the last part, the dynamics of a reaction-diffusion-advection benthic-drift population model that links changes in the flow regime and habitat availability with population dynamics is studied. In the model, the stream is divided into drift zone and benthic zone, and the population is divided into two interacting compartments, individuals residing in the benthic zone and individuals dispersing in the drift zone. The benthic population growth is assumed to be of strong Allee effect type. The influence of flow speed and individual transfer rates between zones on the population persistence and extinction is considered, and the criteria of population persistence or extinction are formulated and proved.

All results are proved rigorously using the theory of partial differential equation, dynamical systems. Various mathematical tools such as bifurcation methods, variational methods, and monotone methods are applied to show the existence of multiple steady state solutions of models.

 

主讲人简介:

王妍,北京师范大学博士后。本科毕业于哈尔滨工业大学(威海),硕士毕业于哈尔滨工业大学。2019年在威廉玛丽学院(美国)获得博士学位。她的研究兴趣包括非线性微分方程和动力学系统,生物学、流行病学中的数学建模等。

 





编辑:哈工大(威海)理学院