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arXiv · 2101.02265

Global dynamics of a Lotka-Volterra competition patch model

Shanshan Chen·Junping Shi·Zhisheng Shuai·Yixiang Wu
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Abstract

The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and cycle-balanced. It is shown 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 system and a graph-theoretic approach based on the Tree-Cycle identity.

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Shanshan Chen, Junping Shi, Zhisheng Shuai, Yixiang Wu. 2021-10-01. Global dynamics of a Lotka-Volterra competition patch model. https://doi.org/10.1088/1361-6544%2Fac3c2e

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