Synchronization of a class of delayed neural networks with reaction–diffusion terms

Wang, Yanyan; Cao, Jinde

doi:10.1016/j.physleta.2007.04.079

Cited by 66 publications

(21 citation statements)

References 30 publications

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“…Thus, the derived sufficient condition includes diffusion terms. We note that, in the proof in the previous articles [24][25][26], a negative integral term with gradient is left out in their deduction. This leads to those criteria that are irrelevant to the diffusion term.…”

Section: Model Description and Preliminariesmentioning

confidence: 96%

“…Therefore, we must consider that the activations vary in space as well as in time. In [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], the authors have considered various dynamical behaviors such as the stability, periodic oscillation, and synchronization of NNs with diffusion terms, which are expressed by partial differential equations. For instance, the authors of [16] discuss the impulsive control and synchronization for a class of delayed reaction-diffusion NNs with the Dirichlet boundary conditions in terms of p-norm.…”

Section: Introductionmentioning

confidence: 99%

“…For instance, the authors of [16] discuss the impulsive control and synchronization for a class of delayed reaction-diffusion NNs with the Dirichlet boundary conditions in terms of p-norm. In [25], the synchronization scheme is discussed for a class of delayed NNs with reaction-diffusion terms. In [26], an adaptive synchronization controller is derived to achieve the exponential synchronization of the drive-response structure of NNs with reaction-diffusion terms.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions

Zhang

2012

Bound Value Probl

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In this article, a delay-differential equation modeling a bidirectional associative memory (BAM) neural networks (NNs) with reaction-diffusion terms is investigated. A feedback control law is derived to achieve the state global exponential synchronization of two identical BAM NNs with reaction-diffusion terms by constructing a suitable Lyapunov functional, using the drive-response approach and some inequality technique. A novel global exponential synchronization criterion is given in terms of inequalities, which can be checked easily. A numerical example is provided to demonstrate the effectiveness of the proposed results.

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Section: Model Description and Preliminariesmentioning

confidence: 96%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions

Zhang

2012

Bound Value Probl

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“…It is different from the traditional linear feedback in [20], where the feedback strength is fixed, thus the strength must be maximal, which means a kind of waste in practice.…”

Section: Remarkmentioning

confidence: 99%

Synchronization of unknown chaotic delayed competitive neural networks with different time scales based on adaptive control and parameter identification

Gan¹,

Xu²,

Kang³

2011

Nonlinear Dyn

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In this paper, we investigate the synchronization problems of delayed competitive neural networks with different time scales and unknown parameters. A simple and robust adaptive controller is designed such that the response system can be synchronized with a drive system with unknown parameters by utilizing Lyapunov stability theory and parameter identification. Our synchronization criteria are easily verified and do not need to solve any linear matrix inequality. This research also demonstrates the effectiveness of application in secure communication. Numerical simulations are carried out to illustrate the main results.

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“…In [20,37], the problem of asymptotic synchronization of delayed reactiondiffusion neural networks was studied with feedback control approach; adaptive exponential synchronization of reaction-diffusion neural networks was discussed in [11]. When Dirichlet boundary conditions of diffusion equation were considered, sufficient synchronization conditions were presented in [7,34,41].…”

Section: Introductionmentioning

confidence: 99%

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

Zou

et al. 2011

Nonlinear Dyn

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In this paper, we are concerned with the synchronization problem of a class of stochastic reaction-diffusion neural networks with time-varying delays and Dirichlet boundary conditions. By using the Lyapunov-Krasovskii functional method, feedback control approach and stochastic analysis technology, delay-dependent synchronization conditions including the information of reaction-diffusion terms are presented, which are expressed in terms of linear matrix inequalities (LMIs). The feedback controllers can be constructed by solving the derived LMIs. Finally, illustrative examples are given to show the effectiveness of the proposed technique.

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Synchronization of a class of delayed neural networks with reaction–diffusion terms

Cited by 66 publications

References 30 publications

Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions

Global exponential synchronization of delayed BAM neural networks with reaction-diffusion terms and the Neumann boundary conditions

Synchronization of unknown chaotic delayed competitive neural networks with different time scales based on adaptive control and parameter identification

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

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