Synchronization of Time-Delayed Chaotic Systems via Modified Adaptive Function Projective Synchronization Method

This article presents a new modified adaptive function projective synchronization method for the synchronization of time-delayed chaotic systems. The adaptive function projective synchronization controller and identification parameter laws are designed on the basis of Lyapunov-Krasovskii functional approach to stabilize the error system which makes the state vector of two chaotic systems asymptotically synchronized. The proposed method is effectively applied to examine the function projective synchronization for the pair of multiple time-delayed Rӧssler System for three different cases. The striking feature of the article is the successful graphical presentation of numerical simulation results, which are carried out by means of Runge-Kutta Method for delay differential equations and clearly demonstrate that the given modified method will be advantageous for getting faster function projective synchronization of time-delay chaotic systems. In this review article the author has carefully revisited an article [1] by Sudheer K. S. and Sabir M (Physics Letter A. 375 1176 (2011)) and claim that the new proposed method is substantially more effective and reliable as compared to the said existing method for synchronizing time-delayed chaotic systems.