Chaos and synchronization of the fractional-order Chua’s system

Zhu, Hao; Zhou, Shangbo; Zhang, Jun

doi:10.1016/j.chaos.2007.06.082

Cited by 97 publications

(34 citation statements)

References 13 publications

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“…In the study by Zhu et al [72], the Laplace transform method was also applied to investigating CS of the following fractional Chua systems with the coupled matrix (k 1 , k 2 , k 3 ), where the drive system is given by …”

Section: Remark 32mentioning

confidence: 99%

Chaos synchronization in fractional differential systems

Zhang

Chen

et al. 2013

Phil. Trans. R. Soc. A.

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This paper presents a brief overview of recent developments in chaos synchronization in coupled fractional differential systems, where the original viewpoints are retained. In addition to complete synchronization, several other extended concepts of synchronization, such as projective synchronization, hybrid projective synchronization, function projective synchronization, generalized synchronization and generalized projective synchronization in fractional differential systems, are reviewed.

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Section: Remark 32mentioning

confidence: 99%

Chaos synchronization in fractional differential systems

Zhang

Chen

et al. 2013

Phil. Trans. R. Soc. A.

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“…For example, chaotic attractors are found in [9] when α = (0.9, 0.9, 0.9) and (a, b, c) = The Jacobian matrix of system (32), evaluated at the equilibrium point x * = (x * , y * , z * ), is…”

Section: Fractional Rössler Systemmentioning

confidence: 99%

“…Recent studies show that chaotic fractional order systems can also be synchronized [19]- [32]. In many literatures, synchronization among fractional order systems is only investigated through numerical simulations that are based on the stability criteria of linear fractional order systems, such as the work presented in [24]- [27], or based on Laplace transform theory, such as the work presented in [28]- [32].…”

Section: Introductionmentioning

confidence: 99%

Adaptive feedback control and synchronization of non-identical chaotic fractional order systems

Odibat

2009

Nonlinear Dyn

152

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To cite this version:Zaid M. Odibat. Adaptive feedback control and synchronization of non-identical chaotic fractional order systems. Nonlinear Dynamics, Springer Verlag, 2009, 60 (4) Abstract This paper addresses the reliable synchronization problem between two non-identical chaotic fractional order systems. In this work, we present an adaptive feedback control scheme for the synchronization of two coupled chaotic fractional order systems with different fractional orders. Based on the stability results of linear fractional order systems and Laplace transform theory, using the master-slave synchronization scheme, sufficient conditions for chaos synchronization are derived. The designed controller ensures that fractional order chaotic oscillators that have nonidentical fractional orders can be synchronized with suitable feedback controller applied to the response system. Numerical simulations are performed to asses the performance of the proposed adaptive controller in synchronizing chaotic systems.

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“…Synchronisation is a particular collective behaviour that may arise in large-scale dynamical systems and has received considerable attention recently [3,4,7,12,22,26,28,38,39]. Synchronisation may be interpreted as a process by which individual systems adjust a given property of their motion to a common behaviour [3].…”

Section: Introductionmentioning

confidence: 99%

Dynamical behaviour of multi-particle large-scale systems

Lopes

Machado

2012

Nonlinear Dyn

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Collective behaviours can be observed in both natural and man-made systems composed of a large number of elemental subsystems. Typically, each elemental subsystem has its own dynamics but, whenever interaction between individuals occurs, the individual behaviours tend to be relaxed, and collective behaviours emerge. In this paper, the collective behaviour of a large-scale system composed of several coupled elemental particles is analysed. The dynamics of the particles are governed by the same type of equations but having different parameter values and initial conditions. Coupling between particles is based on statistical feedback, which means that each particle is affected by the average behaviour of its neighbours. It is shown that the global system may unveil several types of collective behaviours, corresponding to partial synchronisation, characterised by the existence of several clusters of synchronised subsystems, and global synchronisation between particles, where all the elemental particles synchronise completely.

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Chaos and synchronization of the fractional-order Chua’s system

Cited by 97 publications

References 13 publications

Chaos synchronization in fractional differential systems

Chaos synchronization in fractional differential systems

Adaptive feedback control and synchronization of non-identical chaotic fractional order systems

Dynamical behaviour of multi-particle large-scale systems

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