Global dynamics of a Lotka–Volterra competitive system from river ecology: general boundary conditions. (14th February 2020)

• Record Type: Journal Article
• Authors: Xu, Fangfang; Gan, Wenzhen; Tang, De
• Is Part Of: Nonlinearity. Volume 33:Number 4(2020)
• Page Start: 1528
• Page End: 1541
• Publication Date: 2020-02-14
• Subjects: reaction-diffusion-advection -- principal spectral theory -- coexistence steady state; stability -- monotone dynamical systems; 35K57 -- 35K61 -- 37C65 -- 92D25; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab60d8
• Languages: English
• ISSNs: 0951-7715

Abstract

Abstract: In this paper, we mainly study the population dynamics of a Lotka–Volterra competition system from river ecology. One interesting feature in this model concerns the boundary conditions at upstream and downstream ends, where the species can be exposed to a net loss of individuals, as tuned by parameters b u and b d measuring the magnitude of the loss. We establish a complete classification of all possible long time behaviors for this general model, and as an application, we further present a clear picture on the global dynamics by investigating a special case where two species are competing for the same resource.