Adaptive control for anti-synchronization of Chua's chaotic system

Anti-Synchronization of Hyperchaotic Bao and Hyperchaotic Xu Systems via Active Control

“…is used to solve the two systems of differential equations (18) and (19) with the active nonlinear controller (22).…”

Optimisation of the synchronisation of a class of chaotic systems: combination of sliding mode and feedback control

“…Due to the wide potential applications of chaos synchronisation, various synchronisation schemes have been proposed in the last two decades both in theoretical analysis and experimental implementations, such as generalised synchronisation (Murali and Lakshmanan, 1998;Yang and Duan, 1998;Wang and Guan, 2006), phase synchronisation (Michael et al, 1996;Santoboni et al, 2001), lag synchronisation (Taherion et al, 1999;Chen et al, 2007), anti-synchronisation (Li, 2005;Hu et al, 2005;Li and Zhou, 2006) and so on. But despite the amount of theoretical and experimental results already obtained, chaos synchronisation seems difficult task, over all if we think that: 1 due to sensitive dependence of chaos on initial conditions, it is almost impossible to reduce the same starting conditions 2 in matching exactly the master and slave systems, even infinitesimal parametric variations of any model will eventually result in divergence of orbits starting nearby each other 3 parametric differences between chaotic systems (for instance, due to inaccuracy design or time variations) yield different attractors.…”

Coexistence of synchronization and anti-synchronization in chaotic systems

“…Recently, several typical synchronization phenomena have been identified, such as complete synchronization (CS), phase synchronization (PS), lag synchronization (LS), generalized synchronization (GS), anti-phase synchronization (AS), projective synchronization (PS), etc. A variety of works have been devoted to how to realize them (see [2,3,4,5,6,7,8,9,10,11] and the references therein). It is well known that the synchronization between the master (or drive) and the slave system (or response) is equivalent to the globally asymptotically stable (GAS) of the error dynamics e (the difference of the master system and slave system).…”

“…In fact, this necessary condition is not considered in the most of the existing works on anti-synchronization of chaotic systems (See for instance Refs. [8,9,10,11,12,13]). Moreover, the controllers obtained for achieving anti-synchronization of chaotic systems are structurally complex, i.e., some terms in those controllers are needed to counteract the redundant terms, such that E is not the equilibrium point of the error systemĖ = F(y) + F(x).…”