Dynamical study of non-integer order predator–prey system with fear effect

Abstract

This article analyses a fractional order system consisting of two competing species one of which is attacked by the predator. The birth rate of the prey species decreases due to the fear generated by the predator. In our system, we converted the traditional time derivatives to Caputo operator. First, existence and uniqueness are shown. Then, non-negativity and boundedness are examined for our system. The local behaviour near the steady states is investigated. Using the concept of Lyapunov function, global convergence of the solutions is developed. The appearance of bifurcating periodic solutions around the positive equilibrium point is observed. Finally, numerical simulations are conducted to validate the analytical findings.