Coexistence of synchronization and anti-synchronization in chaotic systems

Abstract

The coexistence of anti-synchronization and synchronization in chaotic systems is investigated. A novel algorithm is proposed to determine the variables of the master system that should anti-synchronize with corresponding variables of the slave system. Control strategies that guarantee the coexistence of synchronization and anti-synchronization in the unified chaotic system are presented; while numerical simulations are employed to validate and illustrate the effectiveness of the proposed method.

A Simple Hybrid Synchronization for a Class of Chaotic Financial Systems

“…Here, similar to the previous discussion, we make the following assumptions about error system (18).…”

“…Discrete Dynamics in Nature and Society 7 By using different controller for the error of system (18), the hybrid synchronization effects presented by 2 = ( 1 1 , 0, 0) and 3 = (0, 2 2 , 0) are different. Under the control of 3 = (0, 2 2 , 0) , hybrid synchronization effect of the reaction time is short, and under the control of 2 = ( 1 1 , 0, 0) it is in a long time.…”

“…And so far, in the study of chaos hybrid synchronization problem, there has not been any result of the explicit conditions or algorithms to choose which variables in the driving chaotic system can be synchronized or antisynchronized with the implementation of the corresponding variables in the response chaotic system. Scholars have made some achievements in the chaotic system in hybrid synchronization [17,18], but the hybrid synchronization of the chaotic financial systems is still not perfect so far [15][16][17]. There is still a long wall to go.…”

Hybrid Synchronization of Uncertain Generalized Lorenz System by Adaptive Control

“…Among these schemes, hybrid synchronization is one in which some of the chaotic systems are synchronized whereas others are antisynchronized [9]. Due to its importance, hybrid synchronization has been the subject of many research works [10,11]. Moreover, uncertainties exist widely in engineering and they often bring adverse effects to the stability and performance of real systems.…”

A Four-Dimensional Hyperchaotic Finance System and Its Control Problems

“…Since then, a lot of researchers who are from all kinds of scientific fields had to pay an increasing interest to investigate chaos systems and their relative problems in the past years, and many significant theoretical results and experiments conclusions have been published; for details please see [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] and the references therein. In recent years, several typical kinds of chaos synchronization have been identified, for example, complete synchronization (or synchronization) [14,15], phase synchronization [16,17], lag synchronization [18,19], generalized synchronization [20,21], antisynchronization [22,23], projective synchronization [24,25], coexistence of antisynchronization and complete synchronization [26,27], and simultaneous synchronization 2 Journal of Control Science and Engineering and antisynchronization [27]. However, for the chaotic or hyperchaotic systems, there are still some important questions needed to be further investigated, such as the complexity of the controllers and the existence of some control problems, which partly motivates the present work.…”