AN ANALYTIC STUDY ON CONTROLLING DUFFING CHAOS IN AMPLITUDE DOMAIN AND IN FREQUENCY DOMAIN

摘要

An analytical study on the chaos control of Duffing oscillator both in amplitude domain and in frequency domain is made in this paper. By means of the combined action of harmonically parametrical perturbation and forcing perturbation and suitably adjusting the parameters of perturbations, the chaotic motion of Duffing oscillator can be effectively controlled in a small region in the parametric space. We find that, in the amplitude domain, the chaotic motion exists only in the region where the ratio of the amplitudes of the perturbations is large than critical ratio, and, in the frequency domain, the chaotic motion exists only in a limited region where the frequency of perturbation is lower than superior frequency limit and larger than inferior frequency limit. The inferior frequency limit and superior frequency limit of chaotic region are discovered and determined firstly. An analytical expression of the critical ration of the amplitudes of forcing and parametrical perturbations is established.