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

Jianming Zhang, Lijun Zhang and Yuzhen Bai
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Jianming Zhang: Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
Lijun Zhang: College of Mathematics and Systems Science, Shandong University of Science and Technology Qingdao 266590, China
Yuzhen Bai: School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China

Mathematics, 2019, vol. 7, issue 5, 1-15

Abstract: 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.

Keywords: weak Allee effect; predator-prey system; Hopf bifurcations; stability switches (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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