Global Dynamics of the Lotka-Volterra Competition-Diffusion System: Diffusion and Spatial Heterogeneity I

Xiaoqing He, Wei Ming Ni

Research output: Contribution to journalArticle

58 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)981-1014
Number of pages34
JournalCommunications on Pure and Applied Mathematics
Volume69
Issue number5
DOIs
StatePublished - May 1 2016

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