Almost sure exponential stability of hybrid stochastic delayed Cohen–Grossberg neural networks

2021 ◽  
Author(s):  
Peilin Yu ◽  
Pei Cheng ◽  
Feiqi Deng
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Almost Sure Exponential Stability

scholarly journals LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinearp-Laplace Diffusion

2013 ◽  
Vol 2013 ◽  
pp. 1-21 ◽  
Author(s):  
Ruofeng Rao ◽  
Xiongrui Wang ◽  
Shouming Zhong ◽  
Zhilin Pu
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Schur Complement ◽  
Great Difficulty ◽  
Markovian Jumping ◽  
Robust Exponential Stability ◽  
Almost Sure Exponential Stability ◽  
The Stability ◽  
Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinearp-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods inW1,p(Ω),Itôformula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays.

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.

scholarly journals Stochastic Dynamics of Nonautonomous Cohen-Grossberg Neural Networks

2011 ◽  
Vol 2011 ◽  
pp. 1-17 ◽  
Author(s):  
Chuangxia Huang ◽  
Jinde Cao
Keyword(s):  
Neural Networks ◽  
Lyapunov Function ◽  
Exponential Stability ◽  
Stochastic Stability ◽  
Stochastic Dynamics ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Time Varying ◽  
Almost Sure Exponential Stability ◽  
Moment Exponential Stability

This paper is devoted to the study of the stochastic stability of a class of Cohen-Grossberg neural networks, in which the interconnections and delays are time-varying. With the help of Lyapunov function, Burkholder-Davids-Gundy inequality, and Borel-Cantell's theory, a set of novel sufficient conditions onpth moment exponential stability and almost sure exponential stability for the trivial solution of the system is derived. Compared with the previous published results, our method does not resort to the Razumikhin-type theorem and the semimartingale convergence theorem. Results of the development as presented in this paper are more general than those reported in some previously published papers. An illustrative example is also given to show the effectiveness of the obtained results.

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