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arXiv · 1512.02380

Global dynamics of competition models with nonlocal dispersals I: Symmetric kernels

Xueli Bai·Fang Li
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Abstract

In this paper, the global dynamics of two-species Lotka-Volterra competition models with nonlocal dispersals is studied. Under the assumption that dispersal kernels are symmetric, we prove that except for very special situations, local stability of semi-trivial steady states implies global stability, while when both semi-trivial steady states are locally unstable, the positive steady state exists and is globally stable. Moreover, our results cover the case that competition coefficients are location-dependent and dispersal strategies are mixture of local and nonlocal dispersals.

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Xueli Bai, Fang Li. 2015-12-08. Global dynamics of competition models with nonlocal dispersals I: Symmetric kernels. https://arxiv.org/abs/1512.02380

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