Stability analysis and chaos control in a discrete predator-prey system with Allee effect, fear effect, and refuge

Xiaoming Su; Jiahui Wang; Adiya Bao; Xiaoming Su; Jiahui Wang; Adiya Bao

doi:10.3934/math.2024656

AIMS Mathematics

2024, Volume 9, Issue 5: 13462-13491. doi: 10.3934/math.2024656

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Stability analysis and chaos control in a discrete predator-prey system with Allee effect, fear effect, and refuge

School of Science, Shenyang University of Technology, Shenyang 110870, China

Received: 18 February 2024 Revised: 21 March 2024 Accepted: 01 April 2024 Published: 11 April 2024
MSC : 39A28, 39A30

This paper investigates the complex dynamical behavior of a discrete prey-predator system with a fear factor, a strong Allee effect, and prey refuge. The existence and stability of fixed points in the system are discussed. By applying the central manifold theorem and bifurcation theory, we have established the occurrence of various types of bifurcations, including flip bifurcation and Neimark-Sacker bifurcation. Furthermore, to address the observed chaotic behavior in the system, three controllers were designed by employing state feedback control, OGY feedback control, and hybrid control methods. These controllers serve to control chaos in the proposed system and identify specific conditions under which chaos or bifurcations can be stabilized. Finally, the theoretical analyses have been validated through numerical simulations.
- discrete prey-predator system,
- fear effect,
- Allee effect,
- refuge,
- flip bifurcation,
- Neimark-Sacker bifurcation,
- chaos control
Citation: Xiaoming Su, Jiahui Wang, Adiya Bao. Stability analysis and chaos control in a discrete predator-prey system with Allee effect, fear effect, and refuge[J]. AIMS Mathematics, 2024, 9(5): 13462-13491. doi: 10.3934/math.2024656

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Abstract

This paper investigates the complex dynamical behavior of a discrete prey-predator system with a fear factor, a strong Allee effect, and prey refuge. The existence and stability of fixed points in the system are discussed. By applying the central manifold theorem and bifurcation theory, we have established the occurrence of various types of bifurcations, including flip bifurcation and Neimark-Sacker bifurcation. Furthermore, to address the observed chaotic behavior in the system, three controllers were designed by employing state feedback control, OGY feedback control, and hybrid control methods. These controllers serve to control chaos in the proposed system and identify specific conditions under which chaos or bifurcations can be stabilized. Finally, the theoretical analyses have been validated through numerical simulations.

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