Bifurcation analysis and chaos control of a discrete-time prey-predator model with fear factor

Ceyu Lei; Xiaoling Han; Weiming Wang; Ceyu Lei; Xiaoling Han; Weiming Wang

doi:10.3934/mbe.2022313

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 7: 6659-6679. doi: 10.3934/mbe.2022313

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Research article

Bifurcation analysis and chaos control of a discrete-time prey-predator model with fear factor

Ceyu Lei ¹,
Xiaoling Han ^{1
,
,},
Weiming Wang ^{2
,
,}

1.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
2.
School of Mathematics Science, Huaiyin Normal University, Huaian 223300, China
Acdemic Editor: Baojun Song

Received: 27 March 2022 Revised: 17 April 2022 Accepted: 20 April 2022 Published: 28 April 2022

In this paper, we investigate the complex dynamics of a classical discrete-time prey-predator system with the cost of anti-predator behaviors. We first give the existence and stability of fixed points of this system. And by using the central manifold theorem and bifurcation theory, we prove that the system will experience flip bifurcation and Neimark-Sacker bifurcation at the equilibrium points. Furthermore, we illustrate the bifurcation phenomenon and chaos characteristics via numerical simulations. The results may enrich the dynamics of the prey-predator systems.
- flip bifurcation,
- Neimark-Sacker bifurcation,
- stability analysis,
- fear factor,
- chaos
Citation: Ceyu Lei, Xiaoling Han, Weiming Wang. Bifurcation analysis and chaos control of a discrete-time prey-predator model with fear factor[J]. Mathematical Biosciences and Engineering, 2022, 19(7): 6659-6679. doi: 10.3934/mbe.2022313

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Abstract

In this paper, we investigate the complex dynamics of a classical discrete-time prey-predator system with the cost of anti-predator behaviors. We first give the existence and stability of fixed points of this system. And by using the central manifold theorem and bifurcation theory, we prove that the system will experience flip bifurcation and Neimark-Sacker bifurcation at the equilibrium points. Furthermore, we illustrate the bifurcation phenomenon and chaos characteristics via numerical simulations. The results may enrich the dynamics of the prey-predator systems.

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