Synchronization of Coupled Oscillator Dynamics

Synchronization is most significant phenomena to study the collective behaviour of coupled oscillators. Synchronization is said to occur if phase locking and consensus among corresponding states of coupled dynamical systems is achieved. In general, how to achieve exact conditions for synchronization is unclear. Therefore, it becomes essential to derive conditions on these coupled dynamical systems which lead to synchronization. Here, we aim to derive sufficient conditions for synchronization of selected benchmark oscillators which are linearly coupled. We have used Lyapunov approach to obtain sufficiency condition for synchronization of coupled oscillators. We study synchronization of Van der Pol oscillators and Fitzhugh Nagumo oscillators with all-to-all connectivity, for both uniformly and non-uniformly linearly coupled configurations. These results have been numerically simulated for both the above types of oscillators.