Synchronization threshold of a coupled n-dimensional time-delay system

The synchronization threshold in the general form of one way time-delay system is discussed. The synchronization threshold of coupled time-delay chaotic systems can be estimated by two different analytical approaches. One of them is based on the Krasovskii-Lyapunov theory that represents an extension of the second Lyapunov method for delay differential equations. Another approach uses a perturbation theory of large delay time. Based on the Krasovskii-Lyapunov theory, the deduction process and the application range of the synchronization threshold are given.