Finite-Time Combination-Combination Synchronization for Hyperchaotic Systems

Abstract

A new type of finite-time synchronization with two drive systems and two response systems is presented. Based on the finitetime stability theory, step-by-step control and nonlinear control method, a suitable controller is designed to achieve finite-time combination-combination synchronization among four hyperchaotic systems. Numerical simulations are shown to verify the feasibility and effectiveness of the proposed control technique.

Finite-Time Adaptive Synchronisation of a Class of Master-Slave Systems with Different Unknown Parameters

“…The precise definition of finite-time synchronization, applied to our case of study, is given below [16]:…”

Multi-switching combination synchronization of chaotic systems

“…Further developments in this direction are reported in Refs. [21][22][23][24][25][26][27]; in particular, compound synchronization [28,29], double compound synchronization [30], combination-combination synchronization [23,24,26], finite-time combination-combination synchronization [24][25][26][27], finite-time stochastic combination synchronization [22], hybrid and reduced-order hybrid combination synchronization [31,32] have been proposed and investigated. It is noteworthy that in all these previous works, the goals were to achieve synchronization between state variables of the driver systems and that of identical response system.…”

Generalized compound synchronization of chaos in different orders chaotic Josephson junctions

“…Synchronization and control of coupled chaotic systems have been widely investigated due to their potential applications in many fields such as neural networks, biological networks, secure communication etc. As a result of the diversity and complexity of dynamical behaviours of real complex systems, many kinds of synchronization types and schemes have been developed and investigated, such as complete synchronization [14], anti-synchronization [15], hybrid synchronization [16], projective synchronization [17], projective hybrid synchronization [18], reducedorder synchronization [19], increased order synchronization [20], function projective synchronization [21] combination synchronization [22,23], combination-combination synchronization [24,25], Compound synchronization [26] and so on. Meanwhile, many chaos control and synchronization methods have been proposed to design proper controllers, including feedback control method, adaptive control, active control, open-plus-closed-loop, backstepping, sliding mode control etc [27][28][29][30][31][32].…”

“…Most of the aforementioned works are based on the synchronization scheme which consists of only one drive system and one response system with, thus, limit the flexibility and applicability to real world systems such as in secure communication [25]. Recently, combination synchronization which involves two drive systems and one response system was investigated [22,23].…”

“…Recently, combination synchronization which involves two drive systems and one response system was investigated [22,23]. Also, combination-combination synchronization, where synchronization is achieved between two drive systems and two response systems was implemented, [24,25]. This recently developed synchronization scheme can improve the security of information transmission for example, information signal can be divided into several parts, then each part loaded in each of the different drive systems, and after transmission the original signals is retrieved by combining the received signals of different response systems correctly.…”