Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

Zhou, Xiaobing; Xiong, Lianglin; Cai, Xiaomei

doi:10.1155/2014/953265

Cited by 13 publications

(8 citation statements)

References 23 publications

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“…Further, in Ref. [42], author studied C-C synchronization among four complex nonlinear chaotic systems where it has been recorded that the error synchronization is realized at t = 5 (approx.). Also in Ref.…”

Section: Casementioning

confidence: 99%

“…Further in Ref. [42], C-C synchronization among four complex nonlinear chaotic systems is studied and also particular cases, for instance, projective synchronization and combination synchronization, are mentioned. Moreover, a generalized methodology of C-C synchronization between n-dimensional chaotic fractional order nonlinear dynamical systems is developed in Ref.…”

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confidence: 99%

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Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

Khan

Chaudhary

2020

Arab. J. Math.

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In this paper, we investigate a hybrid projective combination-combination synchronization scheme among four non-identical hyperchaotic systems via adaptive control method. Based on Lyapunov stability theory, the considered approach identifies the unknown parameters and determines the asymptotic stability globally. It is observed that various synchronization techniques, for instance, chaos control problem, combination synchronization, projective synchronization, etc. turn into particular cases of combination-combination synchronization. The proposed scheme is applicable to secure communication and information processing. Finally, numerical simulations are performed to demonstrate the effectivity and correctness of the considered technique by using MATLAB. Mathematics Subject Classification 34K23 • 34K35 • 37B25 • 37N35 1 Introduction Chaos is described as a nonlinear extremely complex phenomenon found in nature featuring the high sensitivity to the initial conditions. These features are defined as butterfly effect, the term coined by Lorenz in 1963. Chaos theory is widely applicable to various fields of applied sciences and engineering, for instance, secure communication [1], biomedical engineering [2], machine learning, circuits [3], finance models [4], jerk systems [5], weather models [6], neural networks [7], oscillations [8], robotics [9], chemical reactions [10], encryption [11], ecological models [12], etc. Consequently, chaos theory has become one of the most appealing fields for researchers and engineers in recent times. Historically, chaos theory dates back to the remarkable work of Poincare [13] established in 1890s while dealing with three-body problem to stabilize the solar system. In fact, he advocated the qualitatively behaviour, using geometric quantitatively to display the universal configuration of all solutions. Despite the observations made by Poincare [13], the first formal introduction of chaos in a deterministic system was proposed by Lorenz [14]. Lorenz observed that simple meteorological models depicted sensitive dependence on the initial conditions, known as butterfly effect, which established that chaos theory is widely applicable in other interdisciplinary areas also. Though the fundamental work on chaos synchronization had been carried by [15], the rapid growth in the field was seen after the phenomenal work of Ott et al. [16]. However, the concept of chaos synchronization was first introduced by Pecora and Carroll [17], wherein they performed synchronization of two identical chaotic systems based on master-slave composition which was unknown for the past 3 decades. Later on, many researchers carried forward the pioneered work of Pecora and Carroll and it has been established that chaos synchronization is also achievable for non-identical chaotic systems possessing absolutely different initial conditions.

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Section: Casementioning

confidence: 99%

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confidence: 99%

Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

Khan

Chaudhary

2020

Arab. J. Math.

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Multi-switching combination synchronization of chaotic systems

2015

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A novel synchronization scheme is proposed for a class of chaotic systems, extending the concept of multi-switching synchronization to combination synchronization such that the state variables of two or more driving systems synchronize with different state variables of the response system, simultaneously. The new scheme, multi-switching combination synchronization (MSCS), represents a significant extension of earlier multi-switching schemes in which two chaotic systems, in a driver-response configuration, are multi-switched to synchronize up to a scaling factor. In MSCS, the chaotic driving systems multi-switch a response chaotic system in combination synchronization. For certain choices of the scaling factors, MSCS reduces to multi-switching synchronization, implying that the latter is a special case of MSCS. A theoretical approach to control design, based on backstepping, is presented and validated using numerical simulations.

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“…Since Fowler et al [1] introduced the complex Lorenz equations, complex systems have played an important role in many branches of physics, especially for chaos-based secure communication, where the complex variables (doubling the number of variables) increase the contents and security of the transmitted information [2]. The synchronization of complex chaotic systems has attracted great attention in the last decades, such as phase synchronization (PHS) and anti-phase synchronization (APHS) [3], complete synchronization (CS) [4], projective synchronization (PS) and modified projective synchronization (MPS) [5], anti-synchronization (AS) [6,7], modified function projective synchronization (MFPS) [8,9], lag synchronization (LS) [10], anti-lag synchronization [11], full state hybrid projective synchronization (FSHPS) [12], modified projective phase synchronization (MPPS) [13], hybrid modified function projective synchronization (HMFPS) [14], modified projective synchronization with complex scaling factors (CMPS) [15,16], complex function projective synchronization (CFPS) [17], modified function projective lag synchronization [18], combination synchronization [19], combination-combination synchronization [20], etc.…”

Section: Introductionmentioning

confidence: 99%

Complete Synchronization of Coupled Multiple-time-delay Complex Chaotic System with Applications to Secure Communication

Zhang¹

2015

Acta Phys. Pol. B

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Considering that time-delay is frequently encountered in a variety of practical chaotic systems, we investigate the complete synchronization (CS) of coupled multiple-time-delay complex chaotic systems and design the control law by error feedback, which is simple in principle and easy to implement in engineering. A communication scheme is further designed according to chaotic masking. We take coupled multiple-time-delay complex Lorenz system as an example, make simulations and verify the effect of the controllers. The error feedback is extended to complex chaotic systems with multiple-time-delay. The CS of real chaotic systems and complex chaotic systems without time-delay are its special cases.

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Combination-Combination Synchronization of Four Nonlinear Complex Chaotic Systems

Cited by 13 publications

References 23 publications

Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

Hybrid projective combination–combination synchronization in non-identical hyperchaotic systems using adaptive control

Multi-switching combination synchronization of chaotic systems

Complete Synchronization of Coupled Multiple-time-delay Complex Chaotic System with Applications to Secure Communication

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