A General Criterion of Synchronization Stability in Ensembles of Coupled Systems and Its Application

Complete synchronization of N coupled systems with symmetric configurations is studied in this paper. The main idea of the synchronization stability criterion is based on stability analysis of zero solution of linearized dynamical systems. By rigorous theoretical analysis, a general synchronization stability criteria is derived for N coupled systems with the first state variable diffusive coupling. This criterion is convenient for us to explore the synchronization of a class of coupled dynamical systems. Finally, the famous Lorenz system and Hindmarsh-Rose(HR) neuron are used to test our theoretical analysis.

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