Synchronization of coupled Duffing-type oscillator dynamical networks

In this paper, synchronization of a network of the coupled Duffing-type oscillators is considered. By using different methods, two kinds of synchronization are investigated over two graph topologies, one is the global synchronization in the sense of Lyapunov over the directed graph, the other is the exponential synchronization over the undirected graph. Firstly, the global synchronization condition of nonlinear network is obtained by the Lyapunov method. Then the global exponential synchronization condition and its synchronized region of linear network are obtained. Finally, some simulations are given to verify the theoretical results.