Dynamics for a fractional-order predator-prey model with group defense

Abstract

In the present article, a new fractional order predator-prey model with group defense is put up. The dynamical properties such as the existence, uniqueness and boundness of solution, the stability of equilibrium point and the existence of Hopf bifurcation of the involved predator-prey model have been discussed. Firstly, we establish the sufficient conditions that guarantee the existence, uniqueness and boundness of solution by applying Lipschitz condition, inequality technique and fractional order differential equation theory. Secondly, we analyze the existence of various equilibrium points by basic mathematical analysis method and obtain some sufficient criteria which guarantee the locally asymptotically stability of various equilibrium points of the involved predator-prey model with the aid of linearization approach. Thirdly, the existence of Hopf bifurcation of the considered predator-prey model is investigated by using the Hopf bifurcation theory of fractional order differential equations. Finally, simulation results are presented to substantiate the theoretical findings.