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Global Dynamics of the Lotka‐Volterra Competition‐Diffusion System: Diffusion and Spatial Heterogeneity I
Author(s) -
He Xiaoqing,
Ni WeiMing
Publication year - 2016
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21596
Subject(s) - competition (biology) , diffusion , mathematics , dynamics (music) , statistical physics , stability (learning theory) , competition model , spatial heterogeneity , economics , physics , computer science , ecology , thermodynamics , microeconomics , machine learning , acoustics , biology , profit (economics)
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.