Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (2): 103-115.doi: 10.16088/j.issn.1001-6600.2021052801

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Stability of a Prey-predator Model with Migration and Allee Effects

XU Wangjun1, CAO Jinde2, WU Daiyong1, SHEN Chuansheng1*   

  1. 1. School of Mathematics and Physics, Anqing Normal University, Anqing Anhui 246133, China;
    2. School of Mathematics, Southeast University, Nanjing Jiangsu 211189, China
  • Received:2021-05-02 Revised:2021-06-28 Published:2022-05-31

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Abstract: A kind of prey-predator system with Allee effect and artificially controlled migration of predators is studied. The system has a square root functional response function. Firstly, by qualitative analysis of the model, the boundedness of the solution is proved, and the existence of the equilibrium point is analyzed. Sufficient conditions for the local stability of the equilibrium point of the system are obtained. Then, the existence of the Hopf-bifurcation of the equilibrium point is discussed, and the stability and direction of the equilibrium Hopf-bifurcation are studied by calculating the first Lyapunov coefficient. Finally, the correctness of the conclusion is verified by numerical simulation. The results indicate that the Allee effect and artificially controlled migration rate are important for the survival and extinction of prey and predator populations.

Key words: prey-predator model, Allee effect, migration rate, Hopf bifurcation, stability

CLC Number: 

  • Q141
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