Dynamics and bifurcation control of a fractional-order delayed predator–prey model with an omnivore

Document Type : Research Paper

Authors

1 Department of Mathematics, Baghlan University, Pol-e-Khomri, Baghlan, Afghanistan.

2 Department of Applied Mathematics, Shahrekord University, Shahrekord, P.O. Box 115, Iran.

Abstract

In this study, we propose a novel fractional delayed predator-prey model that includes an omnivorous species and explore bifurcation control through a state feedback control strategy. We begin by deriving the characteristic polynomial using the Laplace transform and establish new sufficient conditions for stability analysis and Hopf bifurcation, treating the time delay $ \tau $ as a bifurcation parameter. To address Hopf bifurcation in the uncontrolled system, we design a state feedback controller with time delay. Our results indicate that the time delay $ \tau $ significantly affects the onset of Hopf bifurcation. Additionally, the inclusion of fractional order $ 0<\alpha \leq 1 $ enhances solution stability while adding complexity to dynamics of the model. We find that judicious selection of the feedback gain can delay bifurcation, highlighting the critical role of control effort. To validate our theoretical findings, we present numerical simulations conducted using a modified Adams-Bashforth-Moulton predictor-corrector method. These simulations support our theoretical results and demonstrate the efficacy of our proposed control strategy in managing dynamical behaviors of the model.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 07 October 2024

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History

  • Receive Date: 29 May 2024
  • Revise Date: 28 August 2024
  • Accept Date: 06 October 2024

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