Forced waves and their asymptotic behaviors in a Lotka-Volterra competition model with spatio-temporal nonlocal effect under climate change

Abstract

<abstract><p>In this paper, we propose a modified Lotka-Volterra competition model under climate change, which incorporates both spatial and temporal nonlocal effect. First, the theoretical analyses for forced waves of the model are performed, and the existence of the forced waves is proved by using the cross-iteration scheme combining with appropriate upper and lower solutions. Second, the asymptotic behaviors of the forced waves are derived by using the linearization and limiting method, and we find that the asymptotic behaviors of forced waves are mainly determined by the leading equations. In addition, some typical numerical examples are provided to illustrate the analytical results. By choosing three kinds of different kernel functions, it is found that the forced waves can be both monotonic and non-monotonic.</p></abstract>