Chaos control and synchronization of a Φ6-Van der Pol oscillator

The dynamic behavior of a Phi(6)-Van der Pol oscillator subjected to an external disturbance is studied. Numerical analysis of phase diagrams are presented to observe periodic and chaotic motions and sliding mode control design is used to control chaos effectively. Assuming that the exact model of the oscillator is not known and that position is the only state available for measurements, the controller comprises a sliding-like feedback and an uncertainty estimator. As a potential application of the proposed control strategy, we used it to study the synchronization of two Phi(6)-Van der Pol oscillators with uncertainties. Numerical simulations are provided to illustrate the performance of the proposed control strategy. (C) 2004 Elsevier B.V. All rights reserved.