An Impulsive Multi-delayed Feedback Control Method for Stabilizing Discrete Chaotic Systems

An impulsive multi-delayed feedback control strategy to control the period-doubling bifurcations and chaos in an n dimensional discrete system is proposed. This is an extension of the previous result in which the control method is applicable to the one-dimensional case. Then the application of the control method in a discrete prey–predator model is studied systematically, including the dynamics analysis on the prey–predator model with no control, the bifurcations analysis on the controlled model, and the bifurcations and chaos control effects illustrations. Simulations show that the period-doubling bifurcations and the resulting chaos can be delayed or eliminated completely. And the periodic orbits embedded in the chaotic attractor can be stabilized. Compared with the existed methods, a milder condition is needed for the realization of the proposed method. The condition may be considered as a generic case and we may state that almost all periodic orbits can be stabilized by the proposed method. Besides, the idea of impulsive control makes the implementation of the proposed control method easy. The impulsive interval is embodied in the analytical expression of the stability condition, hence can be chosen qualitatively according to the real needs, which is an extension of the existed related results. The introduction of multi-delay enlarges the domain of the control parameters and makes the selection of the control parameters have many choices, and hence become flexible.