Chaos control and synchronization in a fractional neuron network system

Zhou, Shangbo; Li, Hua; Zhu, Zhengzhou

doi:10.1016/j.chaos.2006.07.033

Cited by 128 publications

(29 citation statements)

References 20 publications

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“…[19][20][21][22] discussed chaos and synchronization of the fractional-order neural networks, but these are only numerical simulations. Here, theoretical proof is proposed.…”

Section: Resultsmentioning

confidence: 99%

Synchronization of a Class of Fractional-Order Chaotic Neural Networks

Chen

Chai

et al. 2013

Entropy

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Abstract:The synchronization problem is studied in this paper for a class of fractional-order chaotic neural networks. By using the Mittag-Leffler function, M-matrix and linear feedback control, a sufficient condition is developed ensuring the synchronization of such neural models with the Caputo fractional derivatives. The synchronization condition is easy to verify, implement and only relies on system structure. Furthermore, the theoretical results are applied to a typical fractional-order chaotic Hopfield neural network, and numerical simulation demonstrates the effectiveness and feasibility of the proposed method.

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“…[19][20][21][22] discussed chaos and synchronization of the fractional-order neural networks, but these are only numerical simulations. Here, theoretical proof is proposed.…”

Section: Resultsmentioning

confidence: 99%

Synchronization of a Class of Fractional-Order Chaotic Neural Networks

Chen

Chai

et al. 2013

Entropy

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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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“…We have discussed its chaotic phenomenon and its chaotic synchronization [25] In this paper, we will consider the varying time delay in the following fractional-order neural network model: d a yðtÞ dt a ¼ ÀyðtÞ þ a½f ðyðtÞÞ À bf ðyðt À sðtÞÞÞ;…”

Section: Introductionmentioning

confidence: 99%