Stability and Hopf Bifurcation Analysis of a Fractional-order Leslie-Gower Prey-predator-parasite System with Delay

Abstract

A fractional-order Leslie-Gower prey-predator-parasite system with delay is proposed in this article. The existence and uniqueness of the solutions, as well as their non-negativity and boundedness, are studied. Based on the characteristic equations and the conditions of stability and Hopf bifurcation, the local asymptotic stability of each equilibrium point and Hopf bifurcation of interior equilibrium point are investigated. Moreover, a Lyapunov function is constructed to prove the global asymptotic stability of the infection-free equilibrium point. Lastly, numerical examples are studied to verify the validity of the obtained newly results