Stability and bifurcation in a two-patch model with additive Allee effect

Lijuan Chen; Tingting Liu; Fengde Chen; Lijuan Chen; Tingting Liu; Fengde Chen

doi:10.3934/math.2022034

AIMS Mathematics

2022, Volume 7, Issue 1: 536-551. doi: 10.3934/math.2022034

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Research article

Stability and bifurcation in a two-patch model with additive Allee effect

College of Mathematics and Computer Science, Fuzhou University, Fuzhou, Fujian 350108, China

Received: 15 June 2021 Accepted: 10 August 2021 Published: 14 October 2021
MSC : 34C25, 92D25, 34D20, 34D40

A two-patch model with additive Allee effect is proposed and studied in this paper. Our objective is to investigate how dispersal and additive Allee effect have an impact on the above model's dynamical behaviours. We discuss the local and global asymptotic stability of equilibria and the existence of the saddle-node bifurcation. Complete qualitative analysis on the model demonstrates that dispersal and Allee effect may lead to persistence or extinction in both patches. Also, combining mathematical analysis with numerical simulation, we verify that the total population abundance will increase when the Allee effect constant $ a $ increases or $ m $ decreases. And the total population density increases when the dispersal rate $ D_{1} $ increases or the dispersal rate $ D_{2} $ decreases.
- additive Allee effect,
- dispersal,
- stability,
- bifurcation,
- extinction
Citation: Lijuan Chen, Tingting Liu, Fengde Chen. Stability and bifurcation in a two-patch model with additive Allee effect[J]. AIMS Mathematics, 2022, 7(1): 536-551. doi: 10.3934/math.2022034

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Abstract

A two-patch model with additive Allee effect is proposed and studied in this paper. Our objective is to investigate how dispersal and additive Allee effect have an impact on the above model's dynamical behaviours. We discuss the local and global asymptotic stability of equilibria and the existence of the saddle-node bifurcation. Complete qualitative analysis on the model demonstrates that dispersal and Allee effect may lead to persistence or extinction in both patches. Also, combining mathematical analysis with numerical simulation, we verify that the total population abundance will increase when the Allee effect constant $ a $ increases or $ m $ decreases. And the total population density increases when the dispersal rate $ D_{1} $ increases or the dispersal rate $ D_{2} $ decreases.

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