Open AccessDynamics of a predator-prey model with strong Allee effect and nonconstant mortality rate
Author(s) -
Juan Ye,
AUTHOR_ID,
Yi Wang,
Zhan Jin,
Chuanjun Dai,
Min Zhao,
AUTHOR_ID,
AUTHOR_ID
Publication year - 2022
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2022157
Subject(s) - allee effect , constant (computer programming) , extinction (optical mineralogy) , mathematics , hopf bifurcation , predation , predator , stability (learning theory) , bifurcation , statistical physics , control theory (sociology) , ecology , economics , population , nonlinear system , biology , physics , demography , computer science , paleontology , control (management) , management , quantum mechanics , machine learning , sociology , programming language
In this paper, dynamics analysis for a predator-prey model with strong Allee effect and nonconstant mortality rate are taken into account. We systematically studied the existence and stability of the equilibria, and detailedly analyzed various bifurcations, including transcritical, saddle-node, Hopf and Bogdanov-Takens bifurcation. In addition, the theoretical results are verified by numerical simulations. The results indicate that when the mortality is large, the nonconstant death rate can be approximated to a constant value. However, it cannot be considered constant under small mortality rate conditions. Unlike the extinction of species for the constant mortality, the nonconstant mortality may result in the coexistence of prey and predator for the predator-prey model with Allee effect.