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Taming Chaotic Dynamics With Weak Periodic Perturbations: An Elucidation and Critique.


pdf icon Taming Chaotic Dynamics With Weak Periodic Perturbations: An Elucidation and Critique. (228 K)
Abbadi, Z.; Simiu, E.

Nanotechnology, Vol. 13, No. 2, 153-156, April 2002.

Keywords:

chaotic dynamics; nanoscale technology

Abstract:

Techniques for controlling chaos are needed for, among other applications, control of friction at the nanoscale. According to Braiman and Goldhirsch, the possibility of doing so by adding a weak periodic external forcing to a chaotic system was demonstrated by the results of numerical simulations performed on an asymmetrically multistable system. We discuss those simulations and show that, rather than being a means of controlling chaos, the additional forcing used by Braiman and Goldhirsch has the trival effect of inducing a transition to periodic rotational motion. For the particular case of the system used as an example by these authors the forcing required to achieve this effect is weak because the system parameters were chosen so that height of the potential barrier be correspondingly low.