A Parameter-Perturbation Method for Chaos Control to Stabilizing UPOs

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Abstract: A new method is developed for controlling chaos in discrete systems by perturbing one of its parameters in the neighborhood of an unstable periodic orbit (UPO). For 2-D systems, only two changes in the parameter value are needed in order to stabilize a UPO embedded in the chaotic attractor. The method is general and can be applied to any discrete chaotic system, in which a parameter is accessible and can be changed around a nominal value. To validate and visualize the applicability of the method, an electronic circuit is designed, which resembles the dynamics of the Hénon system, and the control scheme is successfully tested on this circuit. The experimental results show good performance of the method in the presence of noise in the signals, uncertainties in the model, and disturbances in the real circuit system.