Stability and Hopf Bifurcation Analysis of a Predator–Prey Model with Weak Allee Effect Delay and Competition Delay

The purpose of this paper is to study a predator–prey model with Allee effect and double time delays. This research examines the dynamics of the model, with a focus on positivity, existence, stability and Hopf bifurcations. The stability of the periodic solution and the direction of the Hopf bifurca...

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Published inMathematics (Basel) Vol. 12; no. 18; p. 2853
Main Authors Dong, Yurong, Liu, Hua, Wei, Yumei, Zhang, Qibin, Ma, Gang
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2024
Subjects
Allee effect
Analysis
Behavior
Bifurcation theory
Canonical forms
center manifold
Centre manifold theory
Competition
Competition (Biology)
Cooperation
Delay
Ecology
Hopf bifurcation
Population density
Predation
Predation (Biology)
Predator-prey simulation
Predators
Stability
China
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Summary:The purpose of this paper is to study a predator–prey model with Allee effect and double time delays. This research examines the dynamics of the model, with a focus on positivity, existence, stability and Hopf bifurcations. The stability of the periodic solution and the direction of the Hopf bifurcation are elucidated by applying the normal form theory and the center manifold theorem. To validate the correctness of the theoretical analysis, numerical simulations were conducted. The results suggest that a weak Allee effect delay can promote stability within the model, transitioning it from instability to stability. Nevertheless, the competition delay induces periodic oscillations and chaotic dynamics, ultimately resulting in the population’s collapse.
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content type line 14
ISSN:2227-7390
2227-7390
DOI:10.3390/math12182853