Stability of Stochastic Reaction-Diffusion Recurrent Neural Networks with Unbounded Distributed Delays

Stability of reaction-diffusion recurrent neural networks (RNNs) with continuously distributed delays and stochastic influence are considered. Some new sufficient conditions to guarantee the almost sure exponential stability and mean square exponential stability of an equilibrium solution are obtained, respectively. Lyapunov's functional method, M-matrix properties, some inequality technique, and nonnegative semimartingale convergence theorem are used in our approach. The obtained conclusions improve some published results.

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CONVERGENCE DYNAMICS OF STOCHASTIC REACTION–DIFFUSION RECURRENT NEURAL NETWORKS WITH DELAYS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127405013332 ◽

2005 ◽

Vol 15 (07) ◽

pp. 2131-2144 ◽

Cited By ~ 30

Author(s):

JIANHUA SUN ◽

LI WAN

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Recurrent Neural Networks ◽

Sufficient Conditions ◽

Stochastic Perturbation ◽

Reaction Diffusion ◽

Mean Value ◽

Almost Sure Exponential Stability ◽

Transmission Delays ◽

Mean Square Exponential Stability

Stochastic effects on convergence dynamics of reaction–diffusion recurrent neural networks (RNNs) with constant transmission delays are studied. Without assuming the boundedness, monotonicity and differentiability of the activation functions, nor symmetry of synaptic interconnection weights, by skillfully constructing suitable Lyapunov functionals and employing the method of variational parameters, M-matrix properties, inequality technique, stochastic analysis and non-negative semimartingale convergence theorem, delay independent and easily verifiable sufficient conditions to guarantee the almost sure exponential stability, mean value exponential stability and mean square exponential stability of an equilibrium solution associated with temporally uniform external inputs to the networks are obtained, respectively. The results are compared with the previous results derived in the literature for discrete delayed RNNs without diffusion or stochastic perturbation. Two examples are also given to demonstrate our results.

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Exponential Stability of Stochastic Reaction-Diffusion Neural Networks with Mixed Delays in Procurement of Maintenance Material

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.105-107.2315 ◽

2011 ◽

Vol 105-107 ◽

pp. 2315-2320

Author(s):

Xiao Chen

Keyword(s):

Neural Networks ◽

Time Delay ◽

Exponential Stability ◽

Effective Means ◽

Sufficient Conditions ◽

Reaction Diffusion ◽

Functional Method ◽

Mixed Delays ◽

The Neural Network ◽

Discrete Time Delay

In order to effectively improve the equipment maintenance material procurement management efficiency, improve economic efficiency of using the procurement funds, strengthen mathematical theory applications in the area of procurement, the neural network used in evaluation of organizational change is one of the most effective means. In this paper, a class of stochastic Cohen–Grossberg neural networks with reaction-diffusion terms, discrete time delay and distributed time delay is investigated. First, we describe the modeling, illuminate the significance of the system and introduce some preliminary definitions and lemmas which will be employed throughout the paper. Then, by using the Lyapunov functional method, M-matrix properties, nonnegative semimartingale convergence theorem and some inequality technique, sufficient conditions are obtained to guarantee the exponential stability of the system.

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EXPONENTIAL STABILITY OF STOCHASTIC FUZZY CELLULAR NEURAL NETWORKS WITH DISTRIBUTED DELAYS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127409024827 ◽

2009 ◽

Vol 19 (10) ◽

pp. 3387-3395 ◽

Cited By ~ 2

Author(s):

LIPING CHEN ◽

RANCHAO WU

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Lyapunov Functional ◽

Equilibrium Solution ◽

Sufficient Conditions ◽

Cellular Neural Networks ◽

Distributed Delays ◽

Fuzzy Cellular Neural Networks ◽

Mean Square Exponential Stability ◽

Inequality Techniques

The exponential stability of a class of stochastic fuzzy cellular neural networks with distributed delays is investigated in this paper. By using analytic methods such as Lyapunov functional, Itô's formula, inequality techniques and non-negative semimartingale convergence theorem, the sufficient conditions guaranteeing the almost sure and mean square exponential stability of its equilibrium solution are respectively obtained. For illustration, an example is given to show the feasibility of results.

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Exponential stability for stochastic reaction–diffusion BAM neural networks with time-varying and distributed delays

Applied Mathematics and Computation ◽

10.1016/j.amc.2010.12.077 ◽

2011 ◽

Vol 217 (13) ◽

pp. 6078-6091 ◽

Cited By ~ 62

Author(s):

Quanxin Zhu ◽

Xiaodi Li ◽

Xinsong Yang

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Reaction Diffusion ◽

Distributed Delays ◽

Time Varying ◽

Bam Neural Networks ◽

Stochastic Reaction

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IMPROVED SUFFICIENT CONDITIONS FOR GLOBAL EXPONENTIAL STABILITY OF RECURRENT NEURAL NETWORKS WITH DISTRIBUTED DELAYS

International Journal of Bifurcation and Chaos ◽

10.1142/s021812740802152x ◽

2008 ◽

Vol 18 (07) ◽

pp. 2029-2037

Author(s):

WEI WU ◽

BAO TONG CUI ◽

ZHIGANG ZENG

Keyword(s):

Neural Network ◽

Neural Networks ◽

Exponential Stability ◽

Recurrent Neural Networks ◽

Sufficient Conditions ◽

Hopfield Neural Network ◽

Cellular Neural Network ◽

Distributed Delays ◽

Globally Exponential Stability ◽

Exponentially Stable

In this paper, the globally exponential stability of recurrent neural networks with continuously distributed delays is investigated. New theoretical results are presented in the presence of external stimuli. It is shown that the recurrent neural network is globally exponentially stable, and the estimated location of the equilibrium point can be obtained. As typical representatives, the Hopfield neural network (HNN) and the cellular neural network (CNN) are examined in detail. Comparison between our results and the previous results admits the improvement of our results.

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Periodic solutions and its exponential stability of reaction–diffusion recurrent neural networks with continuously distributed delays

Nonlinear Analysis Real World Applications ◽

10.1016/j.nonrwa.2005.01.004 ◽

2006 ◽

Vol 7 (1) ◽

pp. 65-80 ◽

Cited By ~ 98

Author(s):

Qiankun Song ◽

Jinde Cao ◽

Zhenjiang Zhao

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Periodic Solutions ◽

Recurrent Neural Networks ◽

Reaction Diffusion ◽

Distributed Delays

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EXPONENTIAL STABILITY OF REACTION–DIFFUSION FUZZY RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127407018890 ◽

2007 ◽

Vol 17 (09) ◽

pp. 3099-3108 ◽

Cited By ~ 7

Author(s):

QINGHUA ZHOU ◽

LI WAN ◽

JIANHUA SUN

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Recurrent Neural Networks ◽

Sufficient Conditions ◽

Reaction Diffusion ◽

Time Varying ◽

Matrix Properties ◽

Inequality Technique ◽

Delay Dependent ◽

Theoretical Results

Exponential stability of reaction–diffusion fuzzy recurrent neural networks (RDFRNNs) with time-varying delays are considered. By using the method of variational parameters, M-matrix properties and inequality technique, some delay-independent or delay-dependent sufficient conditions for guaranteeing the exponential stability of an equilibrium solution are obtained. One example is given to demonstrate the theoretical results.

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MEAN VALUE EXPONENTIAL STABILITY OF STOCHASTIC REACTION–DIFFUSION GENERALIZED COHEN–GROSSBERG NEURAL NETWORKS WITH TIME-VARYING DELAY

International Journal of Bifurcation and Chaos ◽

10.1142/s021812740701897x ◽

2007 ◽

Vol 17 (09) ◽

pp. 3219-3227 ◽

Cited By ~ 12

Author(s):

LI WAN ◽

QINGHUA ZHOU ◽

JIANHUA SUN

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Sufficient Conditions ◽

Reaction Diffusion ◽

Mean Value ◽

Time Varying ◽

Time Varying Delay ◽

The Stability ◽

Stochastic Reaction ◽

Varying Delay

Stochastic effects on the stability property of reaction–diffusion generalized Cohen–Grossberg neural networks (GDCGNNs) with time-varying delay are considered. By skillfully constructing suitable Lyapunov functionals and employing the method of variational parameters, inequality technique and stochastic analysis, the delay independent and easily verifiable sufficient conditions to guarantee the mean-value exponential stability of an equilibrium solution associated with temporally uniform external inputs to the networks are obtained. One example is given to illustrate the theoretical results.

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ALMOST SURE EXPONENTIAL STABILITY OF STOCHASTIC RECURRENT NEURAL NETWORKS WITH TIME-VARYING DELAYS

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127410025594 ◽

2010 ◽

Vol 20 (02) ◽

pp. 539-544 ◽

Cited By ~ 1

Author(s):

LI WAN ◽

QINGHUA ZHOU

Keyword(s):

Neural Networks ◽

Exponential Stability ◽

Recurrent Neural Networks ◽

Sufficient Conditions ◽

Time Varying ◽

Almost Sure Exponential Stability ◽

The Stability

The stability of stochastic recurrent neural networks with time-varying delays is investigated. A set of novel sufficient conditions on almost sure exponential stability has been established. Two examples are also given to illustrate the effectiveness of our results.

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