Synchronization of coupled time-delay systems: Analytical estimations

The synchronization threshold of coupled time-delay chaotic systems is 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. The analytical expression relating synchronization threshold to the maximal Lyapunov exponent of uncoupled driving and response subsystems is derived. The analytical results are compared with the numerical simulations for two coupled Mackey-Glass systems.