Global Dynamics of the Lotka‐Volterra Competition‐Diffusion System: Diffusion and Spatial Heterogeneity I
Xiaoqing He, Wei‐Ming Ni
Source abstract
Abstract In the first part of this series of three papers, we investigate the combined effects of diffusion, spatial variation, and competition ability on the global dynamics of a classical Lotka‐Volterra competition‐diffusion system. We establish the main results that determine the global asymptotic stability of semitrivial as well as coexistence steady states. Hence a complete understanding of the change in dynamics is obtained immediately. Our results indicate/confirm that, when spatial heterogeneity is included in the model, “diffusion‐driven exclusion” could take place when the diffusion rates and competition coefficients of both species are chosen appropriately.© 2016 Wiley Periodicals, Inc.
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