Global stability of a fractional-order Gause-type predator-prey model with threshold harvesting policy in predator

Hasan S. Panigoro, Agus Suryanto, Wuryansari Muharini Kusumawinahyu, Isnani Darti

Abstract


Lyapunov function gives a major contribution in studying the dynamics of biological models. In this paper, we study the global stability of a fractional-order Gause-type predator-prey model with threshold harvesting policy in predator by using Lyapunov function. We initiate our work by investigating the existence and uniqueness of solution, and then prove the non-negativity and boundedness of solution. Furthermore, we show that the model has four equilibrium points, where the non-trivial equilibrium points are conditionally globally asymptotically stable. At the end, we demonstrate some numerical simulations by using the generalized Adam–Basforth–Moulton method to support theoretical results. We show numerically that the conversion efficiency rate of predation and the order of the derivative influence the dynamics of the model. We also present the existence of forward and Hopf bifurcation numerically driven by conversion efficiency rate of predation and the order of the derivative respectively.

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Published: 2021-07-20

How to Cite this Article:

Hasan S. Panigoro, Agus Suryanto, Wuryansari Muharini Kusumawinahyu, Isnani Darti, Global stability of a fractional-order Gause-type predator-prey model with threshold harvesting policy in predator, Commun. Math. Biol. Neurosci., 2021 (2021), Article ID 63

Copyright © 2021 Hasan S. Panigoro, Agus Suryanto, Wuryansari Muharini Kusumawinahyu, Isnani Darti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

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