Mean square exponential stability of impulsive stochastic reaction-diffusion Cohen–Grossberg neural networks with delays

2012 ◽  
Vol 82 (8) ◽  
pp. 1531-1543 ◽  
Author(s):  
Dingshi Li ◽  
Danhua He ◽  
Daoyi Xu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Reaction Diffusion ◽  
Mean Square ◽  
Mean Square Exponential Stability ◽  
Stochastic Reaction

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.

Mean-Square Exponential Stability of Stochastic Interval Cellular Neural Networks with Time-Varying Delay

2013 ◽  
Vol 760-762 ◽  
pp. 1742-1747
Author(s):  
Jin Fang Han
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Cellular Neural Networks ◽  
Time Varying ◽  
Mean Square ◽  
Razumikhin Theorem ◽  
Time Varying Delay ◽  
Mean Square Exponential Stability ◽  
The Mean ◽  
Varying Delay

This paper is concerned with the mean-square exponential stability analysis problem for a class of stochastic interval cellular neural networks with time-varying delay. By using the stochastic analysis approach, employing Lyapunov function and norm inequalities, several mean-square exponential stability criteria are established in terms of the formula and Razumikhin theorem to guarantee the stochastic interval delayed cellular neural networks to be mean-square exponential stable. Some recent results reported in the literatures are generalized. A kind of equivalent description for this stochastic interval cellular neural networks with time-varying delay is also given.

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