Global dynamics of a Lotka–Volterra competition patch model*

作者：Shanshan Chen, Junping Shi, Zhisheng Shuai, Yixiang Wu · 发表于：Nonlinearity · 年份：2021 · DOI：10.1088/1361-6544/ac3c2e · 被引用次数：45 · 研究领域：Mathematical and Theoretical Epidemiology and Ecology Models、Ecosystem dynamics and resilience、Ecology and Vegetation Dynamics Studies

Abstract The global dynamics of the two-species Lotka–Volterra competition patch model with asymmetric dispersal is classified under the assumptions that the competition is weak and the weighted digraph of the connection matrix is strongly connected and cycle-balanced. We show that in the long time, either the competition exclusion holds that one species becomes extinct, or the two species reach a coexistence equilibrium, and the outcome of the competition is determined by the strength of the inter-specific competition and the dispersal rates. Our main techniques in the proofs follow the theory of monotone dynamical systems and a graph-theoretic approach based on the tree-cycle identity.