Taming chaotic dynamics with weak periodic perturbations: an elucidation and critique

It has been pointed out that a chaos control technique wherein a weak excitation is added to the system could be useful for the control of friction at the nanoscale. We examine the claim that this technique can achieve chaos control even though the added excitation is weak. We show that this claim is only valid for the particular case of systems with very shallow potential wells. However, the applicability of the technique is more general provided that the added periodic force is not restricted to being weak. (Some figures in this article are in colour only in the electronic version)