Stability and bifurcation analysis of a two-patch model with Allee effect and dispersal

TL;DR

This paper analyzes a two-patch ecological model with Allee effect and dispersal, exploring stability, bifurcations, and the impact of dispersal types on species persistence in both ODE and PDE frameworks.

Contribution

It introduces a novel two-patch model incorporating nonlinear dispersal and Allee effect, extending analysis from ODE to PDE, and compares linear and nonlinear dispersal impacts.

Findings

High dispersal intensity can hinder species persistence when Allee effect is large.

Nonlinear diffusion favors population survival more than linear diffusion under large Allee effect.

PDE analysis extends discrete patch results to continuous spatial domains.

Abstract

In the current manuscript, a first two-patch model with Allee effect and nonlinear dispersal is presented. We study both the ODE case and the PDE case here. In the ODE model, the stability of the equilibrium points and the existence of saddle-node bifurcation are discussed. The phase diagram and bifurcation curve of our model are also given by numerical simulation. Besides, the corresponding linear dispersal case is also presented. We show that when the Allee effect is large, high intensity of linear dispersal is not favorable to the persistence of the species. We further show when the Allee effect is large, nonlinear diffusion is more favorable to the survival of the population than linear diffusion. Moreover, the results of the PDE model extends our findings from discrete patches to continuous patches.