Asymptotic population abundance of a two-patch system with asymmetric diffusion
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.
Citation Information
Publication Year | 2020 |
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Title | Asymptotic population abundance of a two-patch system with asymmetric diffusion |
DOI | 10.3934/dcds.2020031 |
Authors | Mengting Fang, Yuanshi Wang, Mingshu Chen, Donald L. DeAngelis |
Publication Type | Article |
Publication Subtype | Journal Article |
Series Title | Discrete & Continuous Dynamical Systems-A |
Index ID | 70206284 |
Record Source | USGS Publications Warehouse |
USGS Organization | Wetland and Aquatic Research Center |