Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction–diffusion terms

Balasubramaniam, P.; Vidhya, C.

doi:10.1016/j.cam.2010.05.007

Cited by 74 publications

(32 citation statements)

References 35 publications

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“…The method used in this paper is different from the previous approaches such as the LMIs technique and the matrix decomposition (see [3], [11], [12], [18], [26], [48]- [53]). It is well known that the LMIs have some advantage.…”

Section: Discussionmentioning

confidence: 99%

Dynamical Behavior of Delayed Reaction–Diffusion Hopfield Neural Networks Driven by Infinite Dimensional Wiener Processes

Liang

Wang

et al. 2016

IEEE Trans. Neural Netw. Learning Syst.

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In this paper, we focus on the long time behavior of the mild solution to delayed reaction-diffusion Hopfield neural networks (DRDHNNs) driven by infinite dimensional Wiener processes. We analyze the existence, uniqueness, and stability of this system under the local Lipschitz function by constructing an appropriate Lyapunov-Krasovskii function and utilizing the semigroup theory. Some easy-to-test criteria affecting the well-posedness and stability of the networks, such as infinite dimensional noise and diffusion effect, are obtained. The criteria can be used as theoretic guidance to stabilize DRDHNNs in practical applications when infinite dimensional noise is taken into consideration. Meanwhile, considering the fact that the standard Brownian motion is a special case of infinite dimensional Wiener process, we undertake an analysis of the local Lipschitz condition, which has a wider range than the global Lipschitz condition. Two samples are given to examine the availability of the results in this paper. Simulations are also given using the MATLAB.

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Section: Discussionmentioning

confidence: 99%

Dynamical Behavior of Delayed Reaction–Diffusion Hopfield Neural Networks Driven by Infinite Dimensional Wiener Processes

Liang

Wang

et al. 2016

IEEE Trans. Neural Netw. Learning Syst.

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“…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%

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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“…The existence of time delays may lead to oscillation, divergence or instability of dynamical systems [2,3]. Various types of time-delay systems have been investigated, and many significant results have been reported [4][5][6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

The stabilization of BAM neural networks with time-varying delays in the leakage terms via sampled-data control

Yang

Lin

2015

Neural Comput & Applic

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This paper is concerned with the stabilization of bidirectional associative memory neural networks with time-varying delays in the leakage terms using sampleddata control. We apply an input delay approach to change the sampling system into a continuous time-delay system. Based on the Lyapunov theory, some stability criteria are obtained. These conditions are expressed in terms of linear matrix inequalities and can be solved via standard numerical software. Finally, one numerical example is given to demonstrate the effectiveness of the proposed results.

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Global asymptotic stability of stochastic BAM neural networks with distributed delays and reaction–diffusion terms

Cited by 74 publications

References 35 publications

Dynamical Behavior of Delayed Reaction–Diffusion Hopfield Neural Networks Driven by Infinite Dimensional Wiener Processes

Dynamical Behavior of Delayed Reaction–Diffusion Hopfield Neural Networks Driven by Infinite Dimensional Wiener Processes

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

The stabilization of BAM neural networks with time-varying delays in the leakage terms via sampled-data control

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