Generalized synchronization of coupled Duffing oscillators: an LMI based approach

In this study, the generalized synchronization of coupled periodically driven duffing oscillators is investigated through Linear Matrix Inequality (LMI) approaches. We first examine the complete synchronization between master-slave Duffing oscillators by converting it to the test of absolute stability of the corresponding error dynamics that possess a standard form of Lur´e system in nonlinear system theory. Anticipating synchronization between time-delayed oscillators is then explored. The obtained LMI condition is based on the delay-dependent stability of time-delay systems, and it allows one to predict the dynamic features of duffing oscillators using a copy of the same system that performs as a slave. Finally, we show the effectiveness of the proposed criteria through two numerical examples.