Generalized Synchronization of Time-Delayed Differential Systems

Jian-Yi, Jing; Lee, Min

doi:10.1088/0256-307x/26/2/028702

Cited by 3 publications

(1 citation statement)

References 42 publications

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“…[8][9][10][11] Since the pioneering works of Pecora and Carroll, [12,13] many researchers paid attention to the synchronization of dynamical systems. [14][15][16][17][18][19][20][21][22][23][24][25] Neural networks (NNs) have been widely studied, as they have massive applications in signal processing, pattern recognition, static image processing, associative memory, and combinatorial optimization. The occurrence of unpredictable behaviors including stable equilibria, periodic oscillations, bifurcation, and chaotic attractors mainly depends on the network's parameters and time delays.…”

Section: Introductionmentioning

confidence: 99%

Impulsive effect on exponential synchronization of neural networks with leakage delay under sampled-data feedback control

Lakshmanan¹,

Park²,

Rihan³

et al. 2014

Chinese Phys. B

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We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov-Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.

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Section: Introductionmentioning

confidence: 99%

Impulsive effect on exponential synchronization of neural networks with leakage delay under sampled-data feedback control

Lakshmanan¹,

Park²,

Rihan³

et al. 2014

Chinese Phys. B

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Linear and nonlinear generalized consensuses of multi-agent systems

Guo

et al. 2014

Chinese Phys. B

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Consensus in directed networks of multiple agents, as an important topic, has become an active research subject. Over the past several years, some types of consensus problems have been studied. In this paper, we propose a novel type of consensus, the generalized consensus (GC), which includes the traditional consensus, the anti-consensus, and the cluster consensus as its special cases. Based on the Lyapunov's direct method and the graph theory, a simple control algorithm is designed to achieve the generalized consensus in a network of agents. Numerical simulations of linear and nonlinear GC are used to verify the effectiveness of the theoretical analysis.

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Optimization of self-adaptive synchronization and parameters estimation in chaotic Hindmarsh-Rose neuron model

Ma¹,

Wen-Tao²,

Jia-Zhen³

2010

Acta Phys. Sin.

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Optimization of self-adaptive synchronization is investigated to estimate a group of five unknown parameters in one certain chaotic neuron model, which is described by the Hindmarsh-Rose. Two controllable gain coefficients are introduced into the Lyapunov function, which is necessary to get the form of parameter observers and controllers for parameter estimation and synchronization, to adjust the transient period for complete synchronization and parameter identification. It is found that the identified results for the minimal parameter （three orders of magnitude less than the maximal parameter） oscillate with time （the estimated results for this parameter is not exact） while the four remaining parameters are estimated very well when one controller and five parameter observers are used to work on the driven system （response system）. To the best of our knowledge, it could result from the great difference of five target parameters （values）. As a result, this problem could be solved when two controllers and five parameter observers are used to change the driven system and all the unknown parameters are identified with high precision. Furthermore, longer transient period for parameter estimation and complete synchronization is required when too strong gain coefficients are used, whils parameters can not be estimated exactly if too weak gain coefficients are used. Therefore, appropriate gain coefficients are critical to achieve the shortest transient period for parameter identification and complete synchronization of chaotic systems, and the optimization of gain coefficients depends on the model being studied. Furthermore, it is confirmed by our numerical results that this scheme is effective and reliable to estimate the parameters even if some parameters jump suddenly.

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Generalized Synchronization of Time-Delayed Differential Systems

Cited by 3 publications

References 42 publications

Impulsive effect on exponential synchronization of neural networks with leakage delay under sampled-data feedback control

Impulsive effect on exponential synchronization of neural networks with leakage delay under sampled-data feedback control

Linear and nonlinear generalized consensuses of multi-agent systems

Optimization of self-adaptive synchronization and parameters estimation in chaotic Hindmarsh-Rose neuron model

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