Coexistence of anti-phase and complete synchronization in coupled chen system via a single variable

Parameter Identification and Hybrid Synchronization in an Array of Coupled Chaotic Systems with Ring Connection: An Adaptive Integral Sliding Mode Approach

“…Different synchronization schemes for chaotic systems were studied and investigated [6][7][8][9][10]. Among these schemes, hybrid synchronization [11][12][13][14][15][16][17][18][19] is one in which some of the chaotic systems are synchronized whereas others are antisynchronized. Due to its importance, hybrid synchronization has been the subject of many research works.…”

“…Due to its importance, hybrid synchronization has been the subject of many research works. These works include study of synchronization/antisynchronization for permanent magnet synchronous motors connected in ring topology [11], function projective type synchronization for complex dynamical networks [12], investigation of complete synchronization and antiphase synchronization together [13], hybrid synchronization of networks having heterogeneous systems [14], study of synchronization for fractional-order systems [15], investigation of synchronization for systems with hyperchaotic nature [16,17], and study of synchronization for complex networks [18,19]. Study of hybrid synchronization involves multiple chaotic systems like complete, adaptive, global, projective, and antisynchronization systems [17,[20][21][22][23][24][25][26][27], and synchronization systems in multiple coupled complex networks [28,29].…”

Adaptive - Synchronization of Fractional-Order Chaotic Systems with Nonidentical Structures

“…From then, many kinds of synchronization have been proposed in dynamical systems. For instance, Li et al [5] pointed out that coexistence of complete synchronization in coupled identical Chen systems is by linear control. In [6], they presented an idea of stochastic phase synchronization about the dynamical evolution of the underlying system.…”

Post-Double Hopf Bifurcation Dynamics and Adaptive Synchronization of a Hyperchaotic System

“…Moreover, since the interest into synchronization of hyperchaotic systems has been always increasing, in particular due to its applications in secure communications (in fact the presence of more than one Lyapunov exponent generates more complex dynamics and improves the security), we propose a scheme to synchronize the modified hyperchaotic Chen system via adaptive control. Recently, many methods and techniques have been developed to realize synchronization and control of chaotic systems, see references [17,11,12,7,18,29] and [3] for a review. In the same spirit of [16], in Section 4 we design an adaptive control law and an update rule for uncertain parameters based on Lyapunov stability theory.…”