Global Dynamics of a Lotka–Volterra Competition Diffusion System with Nonlocal Effects
Bang-Sheng Han, Yinghui Yang, Wei-Jian Bo, Huiling Tang
Abstract
This paper is concerned with the global dynamics of a Lotka–Volterra competition diffusion system having nonlocal intraspecies terms. Based on the reconstructed comparison principle and monotone iteration, the existence and uniqueness of the solution for the corresponding Cauchy problem are established. In addition, the spreading speed of the system with compactly supported initial data is considered, which admits uniform upper and lower bounds. Finally, some sufficient conditions for guaranteeing the existence and nonexistence of Turing bifurcation are given, which depend on the intensity of nonlocality. Comparing with the classical Lotka–Volterra competition diffusion system, our results indicate that a nonconstant periodic solution may exist if the nonlocality is strong enough, which are also illustrated numerically.