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

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.