Bifurcation and Controlling Chaos in a Discrete-Time Biological System

The dynamics of a discrete-time food chain model with strong pressure on preys is investigated. The types of equilibria of the system are analyzed using stability theory and bifurcation theory. The route to chaos via Neimark-Sacker bifurcation followed by period-doubling bifurcations of invariant curves is found for some parameter values through numerical simulation. Moreover, the chaos is controlled on the stable periodic period-1 orbit by the improvement of OGY method. It is shown that the number of iterations used to control chaotic motion on a stable periodic orbit is difference, when the selected regulator poles are different. Numerical simulations are presented to illustrate our results based on the theoretical analysis and show the effect of the control method.