Taming Non-autonomous Chaos in Duffing System Using Small Harmonic Perturbation

In this work, three different classes of the excited models of Duffing system have been considered. In the considered Duffing models, for mathematical simplicity, only linear damping term is included. The various parameters values controlling the complex dynamics are so chosen that each of the models exhibit chaotic strange behavior in their corresponding phase-portraits, Poincare surface of sections and bifurcation diagram when excited sinusoidally with an amplitude, F and frequency \(\omega \) . Unlike the usual method of feedback control, we explore the application of non-feedback control by directly adding a weak additional external periodic perturbation of frequency, \(\varOmega \) , to control the chaos in these models. Incorporating such a perturbation term, bifurcation diagram have been reconstructed to ascertain critical values of the perturbation parameters transforming the chaotic response in the foregoing models to regular behavior. The non-feedback control, in the form of additional small harmonic perturbation term involving such critical parameters, has been shown to result in phase portraits showing the effectiveness of controlling the observed complex chaotic dynamics to regular dynamical response.