Asymptotic population abundance of a two-patch system with asymmetric diffusion

Discrete & Continuous Dynamical Systems-A
By: , and 

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Abstract

This paper considers a two-patch system with asymmetric diffusion rates, in which exploitable resources are included. By using dynamical system theory, we exclude periodic solution in the one-patch subsystem and demonstrate its global dynamics. Then we exhibit uniform persistence of the two-patch system and demonstrate uniqueness of the positive equilibrium, which is shown to be asymptotically stable when the diffusion rates are sufficiently large. By a thorough analysis on the asymptotic population abundance, we demonstrate necessary and sufficient conditions under which the asymmetric diffusion rates can lead to the result that total equilibrium population abundance in heterogeneous environments is larger than that in heterogeneous/homogeneous environments with no diffusion, which is not intuitive. Our result extends previous work to the situation of asymmetric diffusion and provides new insights. Numerical simulations confirm and extend our results.

Additional publication details

Publication type Article
Publication Subtype Journal Article
Title Asymptotic population abundance of a two-patch system with asymmetric diffusion
Series title Discrete & Continuous Dynamical Systems-A
DOI 10.3934/dcds.2020031
Edition Online First
Year Published 2019
Language English
Publisher American Institute of Mathematical Sciences
Contributing office(s) Wetland and Aquatic Research Center