Synchronization of coupled oscillators in presence of disturbance and heterogeneity

Disturbance and heterogeneity have a strong influence on coupled oscillator dynamics. In general, strong disturbances and heterogeneity break the robustness of the coupled system. However, the system can be protected against bounded disturbance and parameter mismatch by introducing coupling and achieving synchronization. The present work gives mathematical investigations of coupled oscillators for synchronization in the presence of bounded disturbance, which may be periodic, aperiodic, and chaotic. Also, the synchronization analysis has been carried out for second-order coupled heterogeneous oscillators. The oscillators considered are second-order Van der Pol oscillator and Fitzhugh Nagumo types of oscillators. The Lyapunov stability approach using a quadratic Lyapunov function and non-smooth Lyapunov functions have been used to obtain theoretical bound on the quality of synchronization or asymptotic synchronization depending on the type of oscillators. The numerical simulations supporting the analytical findings are reported.