Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects

Bifurcation Analysis and Chaos Control of a Discrete Fractional-Order Modified Leslie–Gower Model with Nonlinear Harvesting Effects

This paper investigates the dynamical behavior of a discrete fractional-order modified Leslie–Gower model with a Michaelis–Menten-type harvesting mechanism and a Holling-II functional response. We analyze the existence and stability of the nonnegative equilibrium points. For the interior equilibrium...

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Bibliographic Details
Main Authors: Yao Shi, Xiaozhen Liu, Zhenyu Wang
Format: Article
Language:English
Published: MDPI AG 2024-12-01
Series:Fractal and Fractional
Subjects:
discrete fractional modified Leslie–Gower model
bifurcation
Michaelis–Menten-type harvesting
piecewise-constant argument method
chaos control
Online Access:https://www.mdpi.com/2504-3110/8/12/744
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Summary:This paper investigates the dynamical behavior of a discrete fractional-order modified Leslie–Gower model with a Michaelis–Menten-type harvesting mechanism and a Holling-II functional response. We analyze the existence and stability of the nonnegative equilibrium points. For the interior equilibrium points, we study the conditions for period-doubling and Neimark–Sacker bifurcations using the center manifold theorem and bifurcation theory. To control the chaos arising from these bifurcations, two chaos control strategies are proposed. Numerical simulations are performed to validate the theoretical results. The findings provide valuable insights into the sustainable management and conservation of ecological systems.
ISSN:2504-3110

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