Practical time-delay synchronization of a periodically modulated self-excited oscillators with uncertainties.

This paper studies time-delay synchronization of a periodically modulated Duffing Van der Pol (DVP) oscillator subjected to uncertainties with emphasis on complete synchronization. A robust adaptive response system is designed to synchronize with the uncertain drive periodically modulated DVP oscillator. Adaptation laws on the upper bounds of uncertainties are proposed to guarantee the boundedness of both the synchronization error and the estimated feedback coupling gains. Numerical results are presented to check the effectiveness of the proposed synchronization scheme. The results suggest that the linear and nonlinear terms in the feedback coupling play a complementary role in increasing the synchronization regime in the parameter space of the synchronization manifold. The proposed method can be successfully applied to a large variety of physical systems.