Propagation phenomena for a bistable Lotka–Volterra competition system with advection in a periodic habitat

Abstract

This paper is concerned with the following Lotka-Volterra competition system with advection in a periodic habitat ∂u1 ∂t = d 1

The effect of random dispersal on competitive exclusion – A review

“…In the first part of the series [29], it was proved that a bistable pulsating wave exists provided the interpopulation competition rate k and the frequency of the environment µ are both sufficiently large. This existence result, consistent with the aforementioned abstract one [22], confirms the general principle according to which higher dispersal distances destabilize coexistence [13,23].…”

“…In contradistinction with the homogeneous case, the existence of pulsating waves is not systematic: stable periodic coexistence steady states preventing the formation of wave patterns might now exist. A very recent general result by Du, Li and Wu [22] provides conditions on some eigenvalues ensuring the existence of bistable pulsating waves in one-dimensional spatially periodic media, however it remains difficult to convert these abstract conditions into practically verifiable conditions.…”

“…In temporally periodic environments, the existence of a unique bistable pulsating wave was proved in 2013 by Bao and Wang [3] under some conditions on eigenvalues (reminiscent of those for spatially periodic environments [22]). However the sign of the wave speed is completely unknown and, in particular, it is unclear whether the approach developed by Girardin and Nadin to study the very strong competition limit k → +∞ [30,31] can be used again.…”

Global Directed Dynamic Behaviors of a Lotka-Volterra Competition-Diffusion-Advection System

“…For the competition model of two organisms, either both organisms survive or win with the extinction of the other organisms (see [4][5][6]). In 2019, Du et al [7,8] studied a Lotka-Volterra competition system with periodic habitat advection. From a biological point of view, this pulsating travel front provided a way for two competing species to interact in heterogeneous habitats.…”