Feedback control design for Rössler and Chen chaotic systems anti-synchronization

A Simple Hybrid Synchronization for a Class of Chaotic Financial Systems

“…Scholars have also done a lot of related work in the financial system, as well as in the control and synchronization research [8][9][10]. So far, a lot of methods about chaotic synchronization have been presented to prove that the chaotic synchronization method feasibly [11][12][13][14][15], such as driving response synchronization, coupled synchronization, feedback synchronization, impulsive synchronization, and adaptive synchronization, for the study of chaos synchronization problem has been more mature. However, compared with the chaotic synchronization problem, the problem of antisynchronization of chaotic systems is poorly known, so is the hybrid synchronization, and there are few studies in the financial system.…”

“…In a broad sense, the synchronization and antisynchronization of chaotic systems are the special cases of the hybrid synchronization of the chaotic financial systems; that is, all the variables are synchronized or are antisynchronous [16]. In recent years, some scholars have obtained some research results in the antisynchronization of [12][13][14][15], but they are still in the initial stage; many theories are not mature yet. For example, in the study of antisynchronization problems, the equilibrium point of the error systeṁ= ( ) + ( ) is not explicitly stated, if and only if the condition of (− ) = − ( ) is satisfied [13,14], so that the study of the antisynchronization has a lot of research prospects.…”

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).…”

Using discrete-time hyperchaotic-based asymmetric encryption and decryption keys for secure signal transmission

“…In fact, these processes can, not only reach chaos synchronization starting with different initial conditions, but also can be applied to two secure communication channels based on chaotic systems. The proposed stabilizing conditions for nonlinear discrete-time two levels hierarchical systems are based on the Borne and Gentina practical criterion for stability study [18] associated to the forced arrow form matrix for system description [19][20][21][22][23].…”