Suppressing chaos for some nonlinear oscillators

Abstract

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.