Scalar Feedback Control in a Chaotic Prey-Predator System

Scalar feedback control in a chaotic discrete prey predator system is investigated. The existence of the fixed points and the local stability of the positive fixed point are discussed. By using center manifold theorem, it is proved rigorously that the system undergoes the flip bifurcation near the unique positive fixed point. To eliminate the undesirable chaos induced by the flip bifurcation and stabilize the unstable periodic points, scalar feedback control is adopted. It is clear that the control strategies can be obtained analytically. Numerical simulations are presented not only to illustrate the results with the theoretical analysis but also to exhibit the new complex dynamics. The effectiveness of the control method are shown at last.