Abstract
We address the interplay among the intrinsic dynamic structure of chaos, external weak periodic perturbation, and noise. The periodicity and the stability condition of the chaos controlled by a weak periodic perturbation are determined. The results explain why controlling chaos works in the Braiman and Goldhirsch method, and the conditions for the targeted state to be successfully created are presented. The stochastic response of the system when contaminated with a dynamic noise is also derived.
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