Synchronization of chaotic dynamical systems

Chaotic dynamical systems produce signals with unpredictable complexity. Their essential characteristic is that it does not synchronize with any other system. However, they can synchronize provided the sufficiently large coupling is introduced between them. In the present work, the Lyapunov stability analysis has been carried out using non-smooth Lyapunov function to obtain sufficient coupling gain for synchronization. The Mathematical investigations have been done independently for all-to-all coupled Lorenz attractors and all-to-all coupled Rossler attractors. The results in each case are confirmed through numerical simulations.