Narrow Results

In this paper, a criteria of suppressing chaos for a kind of nonlinear oscillators is established by the theory of the strange attractor. The oscillators considered include Duffing, van der Pol, Duffing–van der Pol and pendulum. According to this criteria, we analyze the phase effect using two methods, one by adding the second external force term and the other by adding parametric excitation, both of which may be used to suppress chaos in the systems. Some examples are used to illustrate the validity of the criteria and the importance of phase effect in suppressing chaos.

This article extends the range of applications of a previous paper [Leung & Liu, 2003]. Some new methods to suppress chaos are proposed so that the Melnikov function is modified only slightly for the easy elimination of simple zeros. The reasonability of the methods is analyzed by the previously established criteria. Some examples are also given.

In this paper, theoretical framework and numerical verification for suppressing homoclinic chaos of a class of vibro-impact oscillators are discussed by adding parametric excitations in the form of $xfcos(\omega \tau +\phi )$ as the control item. The analytical Melnikov method for planar vibro-impact systems is employed to obtain the corresponding thresholds of parameters as sufficient conditions for suppressing chaos. Two typical oscillators are presented to show the effectiveness of theoretical analysis for suppressing homoclinic chaos by tuning the amplitudes, frequencies and phases of the parametric excitations.