SYNCHRONIZATION OF COUPLED TIME-DELAY SYSTEMS : ANALYTICAL ESTIMATIONS

Semiconductor Physics Institute, LT-2600 Vilnius, Lithuania~Received 19 March 1998!The synchronization threshold of coupled time-delay chaotic systems is estimated by two different analyticalapproaches. One of them is based on the Krasovskii-Lyapunov theory that represents an extension of thesecond Lyapunov method for delay differential equations. Another approach uses a perturbation theory of largedelay time. The analytical expression relating synchronization threshold to the maximal Lyapunov exponent ofuncoupled driving and response subsystems is derived. The analytical results are compared with the numericalsimulations for two coupled Mackey-Glass systems.@S1063-651X~98!11809-3#PACS number~s!: 05.45.1bI. INTRODUCTION