Chaotic Dynamics and Control of Discrete Ratio-Dependent Predator-Prey System

Abstract

This study examines the complexity of a discrete-time predator-prey system with ratio-dependent functional response. We establish algebraically the conditions for existence of fixed points and their stability. We show that under some parametric conditions the system passes through a bifurcation (flip or Neimark-Sacker). Numerical simulations are presented not only to justify theoretical results but also to exhibit new complex behaviors which include phase portraits, orbits of periods 9, 19, and 26, invariant closed circle, and attracting chaotic sets. Moreover, we measure numerically the Lyapunov exponents and fractal dimension to confirm the chaotic dynamics of the system. Finally, a state feedback control method is applied to control chaos which exists in the system.