Complex dynamics in a discrete-time model of two competing prey with a shared predator

This paper concentrates on the study of a discrete time model of two competing prey with a shared predator. The condition for the existence and local stability of positive fixed point are derived. By using an iteration scheme and the comparison principle of difference equations, it is possible to obtain the sufficient condition for global stability of the positive fixed point. The sufficient criterion for Neimark-Sacker bifurcation and flip bifurcation are established. The system admits chaotic dynamics for a certain choice of the system parameters which is controlled by applying hybrid control method. The intra-specific competition among predators and the intrinsic growth rate of prey species have major impact for different bifurcation. For continuous system, handling time spent for prey population plays an important role for obtaining limit cycle behaviour. The decrease amount of this rate makes the system stable. Global convergence of the solutions to the coexistence equilibrium point is possible for a particular choice of system parameters. The obtained results for discrete system are verified through numerical simulations. Also some diagrams are presented for continuous system.