Stability and Bifurcation Analysis on a Predator–Prey System with the Weak Allee Effect

In this paper, the dynamics of a predator-prey system with the weak Allee effect is considered. The sufficient conditions for the existence of Hopf bifurcation and stability switches induced by delay are investigated. By using the theory of normal form and center manifold, an explicit expression, wh...

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Bibliographic Details
Published in:Mathematics
Main Authors: Jianming Zhang, Lijun Zhang, Yuzhen Bai
Format: Article
Language:English
Published: MDPI AG 2019-05-01
Subjects:
weak Allee effect
predator-prey system
Hopf bifurcations
stability switches
Online Access:https://www.mdpi.com/2227-7390/7/5/432
Description
Summary:In this paper, the dynamics of a predator-prey system with the weak Allee effect is considered. The sufficient conditions for the existence of Hopf bifurcation and stability switches induced by delay are investigated. By using the theory of normal form and center manifold, an explicit expression, which can be applied to determine the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions, are obtained. Numerical simulations are performed to illustrate the theoretical analysis results.
ISSN:2227-7390

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