Synchronization of ring coupled four oscillators

Synchronization bears greater significance for stability of coupled dynamical systems. It represents the adjustment of rhythms among coupled systems in consequence to phase locking and consensus among the corresponding states. In general, exact condition which gives synchronization is not clearly known. The objective of present work, is to achieve sufficient condition for synchronization of ring coupled four oscillators and the same is achieved using Lyapunov approach. The sufficient condition which gives synchronization of benchmark ring coupled oscillators e.g. Van der Pol and Fitzhugh Nagumo neural oscillators have been obtained when they are uniformly linearly coupled in a ring. Also, the numerical simulations of the derived results have been reported.