Stabilization of stochastic Hopfield neural network with distributed parameters

Luo, Qi; Deng, Fujin; Jun-dong, Bao; Zhao, Biao; Fu, Yuli

doi:10.1360/03yf0332

Cited by 34 publications

(28 citation statements)

References 12 publications

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“…Example 2 Consider the following reaction-diffusion neural networks with Dirichlet boundary conditions: and Thus, from Theorem 4, the system of (25) and (26) is almost surely synchronized with the control gains K 1 and K 2 . The dynamical behavior of the synchronization error can be seen in Figs.…”

Section: Illustrative Examplesmentioning

confidence: 99%

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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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Section: Illustrative Examplesmentioning

confidence: 99%

“…Therefore, it is reasonable and significant to take reaction-diffusion effect into full account in the research of neural networks. Many results on stability analysis of reactiondiffusion neural networks have been presented in the literature; see, for example, [5,19,23,25,27,35,36,38,39] and the references therein.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

Zou

et al. 2011

Nonlinear Dyn

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“…Ref. [42] took into account both stochastic factor and diffusion factor and investigated the stability of neural network as follows:…”

Section: Application and Corollarymentioning

confidence: 99%

“…We can prove that the main results of ref. [42] are all the corollaries of this paper and the involved mark can be referred to ref. [42].…”

Section: Application and Corollarymentioning

confidence: 99%

“…Then, for some special kinds of stochastic partial differential systems, we wonder if we can use the peculiarity of systems to overcome the difficulty of wanting Itô's formula or try to establish the corresponding Lyapunov stability theory by indirectly applying Itô's formula? In our recent paper [42] , we discussed the stabilization of stochastic Hopfield neural network with distributed parameters by constructing an average Lyapunov function with respect to spatial variables and applying Itô's formula under the integral operator. It is the same idea that we adopt to establish the Lyapunov stability theory of Itô stochastic reaction diffusion systems in this paper.…”

Section: Introductionmentioning

confidence: 99%

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Theory and application of stability for stochastic reaction diffusion systems

Luo

Deng

Mao

et al. 2008

Sci. China Ser. F-Inf. Sci.

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So far, the Lyapunov direct method is still the most effective technique in the study of stability for ordinary differential equations and stochastic differential equations. Due to the shortage of the corresponding Itô formula, this useful method has not been popularized in stochastic partial differential equations. The aim of this work is to try to extend the Lyapunov direct method to the Itô stochastic reaction diffusion systems and to establish the corresponding Lyapunov stability theory, including stability in probablity, asymptotic stability in probability, and exponential stability in mean square. As the application of the obtained theorems, this paper addresses the stability of the Hopfield neural network and points out that the main results obtained by Holden Helge and Liao Xiaoxin et al. can be all regarded as the corollaries of the theorems presented in this paper

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Adaptive Exponential Synchronization of Stochastic Delay Neural Networks with Reaction-Diffusion

Zhao

Deng

2009

Advances in Neural Networks – ISNN 2009

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Stabilization of stochastic Hopfield neural network with distributed parameters

Cited by 34 publications

References 12 publications

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

Synchronization of stochastic chaotic neural networks with reaction-diffusion terms

Theory and application of stability for stochastic reaction diffusion systems

Adaptive Exponential Synchronization of Stochastic Delay Neural Networks with Reaction-Diffusion

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