Bifurcation analysis and chaos control of a discrete fractional-order Leslie-Gower model with fear factor

Yao Shi; Zhenyu Wang; Yao Shi; Zhenyu Wang

doi:10.3934/math.20241462

AIMS Mathematics

2024, Volume 9, Issue 11: 30298-30319. doi: 10.3934/math.20241462

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Bifurcation analysis and chaos control of a discrete fractional-order Leslie-Gower model with fear factor

Yao Shi ^{1
,
,},
Zhenyu Wang ^{2
,
,}

1.
School of Mathematics and Physics, Hebei University of Engineering, Handan, 056038, China
2.
Department of Mathematics, Harbin Institute of Technology at Weihai, Weihai, 264209, China

Received: 05 September 2024 Revised: 16 October 2024 Accepted: 23 October 2024 Published: 24 October 2024
MSC : 39A28, 39A30, 65P30

This study focused on the dynamical behavior analysis of a discrete fractional Leslie-Gower model incorporating antipredator behavior and a Holling type Ⅱ functional response. Initially, we analyzed the existence and stability of the model's positive equilibrium points. For the interior positive equilibrium points, we investigated the parameter conditions leading to period-doubling bifurcation and Neimark-Sacker bifurcation using the center manifold theorem and bifurcation theory. To effectively control the chaos resulting from these bifurcations, we proposed two chaos control strategies. Numerical simulations were conducted to validate the theoretical results. These findings may contribute to the improved management and preservation of ecological systems.
- discrete fractional Leslie-Gower model,
- stability analysis,
- period-doubling bifurcation,
- Neimark-Sacker bifurcation,
- fear factor,
- chaos control
Citation: Yao Shi, Zhenyu Wang. Bifurcation analysis and chaos control of a discrete fractional-order Leslie-Gower model with fear factor[J]. AIMS Mathematics, 2024, 9(11): 30298-30319. doi: 10.3934/math.20241462

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Abstract

This study focused on the dynamical behavior analysis of a discrete fractional Leslie-Gower model incorporating antipredator behavior and a Holling type Ⅱ functional response. Initially, we analyzed the existence and stability of the model's positive equilibrium points. For the interior positive equilibrium points, we investigated the parameter conditions leading to period-doubling bifurcation and Neimark-Sacker bifurcation using the center manifold theorem and bifurcation theory. To effectively control the chaos resulting from these bifurcations, we proposed two chaos control strategies. Numerical simulations were conducted to validate the theoretical results. These findings may contribute to the improved management and preservation of ecological systems.

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