F. M. Moukam Kakmeni

The nonlinear response and suppression of chaos by weak harmonic perturbation inside a triple well $Φ6$-Rayleigh oscillator combined to parametric excitations is studied in this paper. The main attention is focused on the dynamical properties of local bifurcations as well as global bifurcations including homoclinic and heteroclinic bifurcations. The original oscillator is transformed to averaged equations using the method of harmonic balance to obtain periodic solutions. The response curves show the saddle-node bifurcation and the multi-stability phenomena. Based on the Melnikov’s method, horseshoe chaos is found and its control is made by introducing an external periodic perturbation.

This paper presents a robust control scheme for a class of uncertain chaotic systems. The proposed feedback controller is composed by an uncertainty estimator and a backstepping feedback, so its implementation is quite simple and can be made on the basis of the measured signal. The developed control scheme allows chaos suppression despite uncertainties in the model as well as unmeasured disturbances. The Chua and $Φ6$-Duffing are used to illustrate the performance of the proposed controller.