Exponential stability analysis of stochastic reaction-diffusion Cohen–Grossberg neural networks with mixed delays

2011 ◽  
Vol 74 (17) ◽  
pp. 3084-3091 ◽  
Author(s):  
Quanxin Zhu ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Reaction Diffusion ◽  
Mixed Delays ◽  
Stochastic Reaction

scholarly journals Stability Analysis of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Time-Varying Delays

2009 ◽  
Vol 2009 ◽  
pp. 1-18 ◽  
Author(s):  
Chuangxia Huang ◽  
Xinsong Yang ◽  
Yigang He
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Exponential Stability ◽  
Stochastic Analysis ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Inequality Techniques ◽  
Stochastic Reaction ◽  
Moment Exponential Stability

This paper is concerned withpth moment exponential stability of stochastic reaction-diffusion Cohen-Grossberg neural networks with time-varying delays. With the help of Lyapunov method, stochastic analysis, and inequality techniques, a set of new suffcient conditions onpth moment exponential stability for the considered system is presented. The proposed results generalized and improved some earlier publications.

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

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.

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

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
Chuangxia Huang ◽  
Xinsong Yang ◽  
Yigang He ◽  
Lehua Huang
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Recurrent Neural Networks ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Functional Method ◽  
Distributed Delays ◽  
Almost Sure Exponential Stability ◽  
Mean Square Exponential Stability ◽  
Stochastic Reaction

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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