Global stability for a Lotka-Volterra competition system with symmetric diffusion matrices
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Published on: September 26, 2016
Yizheng Hu1, Xinze Lian2, Zhengyi Lu3
1College of mathematics and physics, Wenzhou University, Wenzhou 325035, China.
Abstract:
The global stability of a two-species Lotka-Volterra competition n-patch system with symmetric diffusion matrices is a conjecture proposed by Hofbauer, So, and Takeuchi. The cases n = 3, 4, 5 have been demonstrated to hold validity. In this article, it is shown that the Hofbauer-So-Takeuchi conjecture holds true for general n. A concrete example is given to display the global stability for one of the equilibria of the system depending on the magnitude of the parameters. Furthermore, an algebraic curve problem in the system's parameter space for determining the stability regions is proposed.
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