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

2015/12/08 by Bai, Xueli, Li, Fang
#45M05 #45M20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 45G15 #Secondary: 45M10

paper · doi:10.48550/arxiv.1512.02380

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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