Dynamical analysis and chaos control in discrete-time prey-predator model

In this work, a discretized two-dimensional Leslie-Gower prey-predator model is investigated. The results for the existence and uniqueness and the conditions for the local asymptotic stability of the solutions are determined. It is also exhibited that the discrete system undergoes Neimark-Sacker, flip and fold bifurcation under certain conditions. The discretized system exhibits wide range of complex dynamical behavior viz. periodicity, quasi periodicity and chaos with respect to different parameters. Further, three control methods: state feedback, pole-placement and hybrid control are deployed to control the chaos in the system. Under certain conditions, chaos and bifurcation of the system are stabilized through the control strategies. The extensive numerical simulation is done to demonstrate the analytical findings.