Projective synchronization in multiple modulated time-delayed systems with adaptive scaling factor

Abstract

In this paper, we propose a nonlinear observer-based stable synchronization in multiple timedelayed systems where the response system states are scaled replicas of the drive system states. It is very difficult to estimate the scaling factor because its dependent on the initial condition and the underlying chaotic dynamics. Based on the nonlinear observer approach, a new adaptive law is proposed to simultaneously estimate the scaling factor and projective synchronization in multiple modulated time-delayed systems. As an example, numerical simulations for the multiple time-delayed Ikeda and Mackey-Glass systems are conducted, which is in good agreement with the theoretical analysis.

Synchronization of time-delayed systems with discontinuous coupling

“…Since the pioneer work of Pecora and Carroll [18], chaos synchronization in coupled systems has been extensively studied in many areas, such as biological systems, information processing, secure communications, economical systems, etc [3]. There are many different kinds of synchronization, such as complete synchronization [24], generalized synchronization [15], anti-synchronization [17], projective synchronization [7], etc.…”

Projective-anticipating, projective and projective-lag synchronization of chaotic systems with time-varying delays

“…However, most existing studies pertaining to different types of projective synchronization in variable time-delayed chaotic systems have mainly focused on exact projective synchronization [20,21]; little attention has been paid to projective-anticipating and projective-lag synchronization. In recent papers [22,23], projective-anticipating, projective and projective-lag synchronization in time-delayed systems with modulated time delays have been studied.…”

Isochronal function projective synchronization between chaotic and time-delayed chaotic systems

“…While results about zero lag time difference between synchronized state shifts, i.e., isochronal synchronization [24,25] are also obtained between time-delayed systems. Note that projective synchronization [26,27] between time-delayed chaotic systems was extensively investigated. However, results about isochronal function projective synchronization between chaotic and time-delayed chaotic systems are still few.…”