Bifurcation Analysis and Chaos Control of a Discrete–Time Fractional Order Predator-Prey Model with Holling Type II Functional Response and Harvesting

Year 2025, Volume: 7 Issue: 1, 87 - 98, 31.03.2025

Agus Suryanto , İsnani Darti , Edi Cahyono

https://doi.org/10.51537/chaos.1581247

Abstract

This paper employs a piecewise constant approximation to discretize a fractional order Holling type II predator-prey model with harvesting in both populations. The dynamics of the resulting discrete-time model are then investigated. First, the conditions for fixed points’ existence and stability are established. It is also demonstrated that the proposed discrete-time model can undergo either flip bifurcation or Neimark-Sacker bifurcation. The existence and direction of both bifurcations have been identified using the center manifold theorem. The appearance of these bifurcations results in the emergence of chaotic dynamics. To stabilize chaos at the fixed point of unstable trajectories, we provide two types of control chaos: hybrid control and state feedback control. By selecting appropriate control settings, it is shown that both hybrid control and state feedback control eliminate chaotic orbits and make the fixed point asymptotically stable. Some numerical simulations were used to verify all analytical conclusions.

Keywords

Discrete-time model, Fractional order, Flip bifurcation, Neimark-Sacker bifurcation, Chaos control

Ethical Statement

Not applicable.

Supporting Institution

Directorate of Research, Technology and Community Service of the Ministry of Education, Culture, Research, and Technology of the Republic of Indonesia

Project Number

00309.11/UN10.A0501/B/PT.01.03.2/2024

Thanks

This research was funded by Directorate of Research, Technology and Community Service of the Ministry of Education, Culture, Research, and Technology of the Republic of Indonesia through Regular Fundamental Research (PFR) [Contract no. 00309.11/UN10.A0501/B/PT.01.03.2/2024].

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