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Open AccessArticle

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

1
Department of Mathematics, School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
2
College of Mathematics and Systems Science, Shandong University of Science and Technology Qingdao 266590, China
3
School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(5), 432; https://doi.org/10.3390/math7050432
Received: 9 April 2019 / Revised: 26 April 2019 / Accepted: 6 May 2019 / Published: 16 May 2019
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. View Full-Text
Keywords: weak Allee effect; predator-prey system; Hopf bifurcations; stability switches weak Allee effect; predator-prey system; Hopf bifurcations; stability switches
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Zhang, J.; Zhang, L.; Bai, Y. Stability and Bifurcation Analysis on a Predator–Prey System with the Weak Allee Effect. Mathematics 2019, 7, 432.

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