Dynamics of a nonlinear discrete predator-prey system with fear effect

Xiongxiong Du; Xiaoling Han; Ceyu Lei; Xiongxiong Du; Xiaoling Han; Ceyu Lei

doi:10.3934/math.20231221

AIMS Mathematics

2023, Volume 8, Issue 10: 23953-23973. doi: 10.3934/math.20231221

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Research article

Dynamics of a nonlinear discrete predator-prey system with fear effect

Department of Mathematics, Northwest Normal University, Lanzhou, 730070, China

Received: 18 May 2023 Revised: 16 July 2023 Accepted: 24 July 2023 Published: 07 August 2023
MSC : 37G15, 37N25, 39A28, 92D25, 93C10

In this paper, we investigate a nonlinear discrete prey-predator system with fear effects. The existence, local stability and boundedness of positive equilibrium point are discussed. Using the center manifold theorem and bifurcation theory, the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation in the interior of $ \mathbb{R}_{+}^{2} $ are established. Furthermore, the numerical simulations not only show complex dynamical behaviors, but also verify our analysis results. A feedback control strategy is employed to control bifurcation and chaos in the system.
- predator-prey system,
- flip bifurcation,
- Neimark-Sacker bifurcation,
- fear factor,
- chaos
Citation: Xiongxiong Du, Xiaoling Han, Ceyu Lei. Dynamics of a nonlinear discrete predator-prey system with fear effect[J]. AIMS Mathematics, 2023, 8(10): 23953-23973. doi: 10.3934/math.20231221

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Abstract

In this paper, we investigate a nonlinear discrete prey-predator system with fear effects. The existence, local stability and boundedness of positive equilibrium point are discussed. Using the center manifold theorem and bifurcation theory, the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation in the interior of $ \mathbb{R}_{+}^{2} $ are established. Furthermore, the numerical simulations not only show complex dynamical behaviors, but also verify our analysis results. A feedback control strategy is employed to control bifurcation and chaos in the system.

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