Open AccessStability and bifurcation in a two-patch model with additive Allee effect
Author(s) -
Lijuan Chen,
Tingting Liu,
Fengde Chen
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2022034
Subject(s) - allee effect , biological dispersal , extinction (optical mineralogy) , population , mathematics , stability (learning theory) , statistical physics , bifurcation , population model , physics , nonlinear system , demography , computer science , quantum mechanics , machine learning , sociology , optics
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.