Stability analysis of stochastic reaction-diffusion delayed neural networks with Levy noise

2011 ◽  
Vol 20 (4) ◽  
pp. 535-541 ◽  
Author(s):  
Jun Peng ◽  
Zaiming Liu
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Reaction Diffusion ◽  
Lévy Noise ◽  
Delayed Neural Networks ◽  
Stochastic Reaction ◽  
Levy Noise

Adaptive state estimation of Markov switched neural networks driven by Lévy noise

2019 ◽  
Vol 42 (2) ◽  
pp. 330-336
Author(s):  
Dongbing Tong ◽  
Qiaoyu Chen ◽  
Wuneng Zhou ◽  
Yuhua Xu
Keyword(s):  
Neural Networks ◽  
State Estimation ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Lévy Noise ◽  
Linear Matrix ◽  
Delayed Neural Networks ◽  
Switched Neural Networks ◽  
Inequality Technique ◽  
Levy Noise

This paper proposes the [Formula: see text]-matrix method to achieve state estimation in Markov switched neural networks with Lévy noise, and the method is very distinct from the linear matrix inequality technique. Meanwhile, in light of the Lyapunov stability theory, some sufficient conditions of the exponential stability are derived for delayed neural networks, and the adaptive update law is obtained. An example verifies the condition of state estimation and confirms the effectiveness of results.

Synchronization of delayed neural networks with Lévy noise and Markovian switching via sampled data

2015 ◽  
Vol 81 (3) ◽  
pp. 1179-1189 ◽  
Author(s):  
Jun Yang ◽  
Wuneng Zhou ◽  
Peng Shi ◽  
Xueqing Yang ◽  
Xianghui Zhou ◽  
...  
Keyword(s):  
Neural Networks ◽  
Markovian Switching ◽  
Lévy Noise ◽  
Sampled Data ◽  
Delayed Neural Networks ◽  
Levy Noise

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.

scholarly journals Stability of Sets Criteria for Impulsive Cohen-Grossberg Delayed Neural Networks with Reaction-Diffusion Terms

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 27 ◽  
Author(s):  
Gani Stamov ◽  
Stefania Tomasiello ◽  
Ivanka Stamova ◽  
Cvetelina Spirova
Keyword(s):  
Neural Networks ◽  
Stability Analysis ◽  
Asymptotic Stability ◽  
Equilibrium State ◽  
Global Exponential Stability ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Delayed Neural Networks ◽  
The Stability ◽  
Impulsive Reaction

The paper proposes an extension of stability analysis methods for a class of impulsive reaction-diffusion Cohen-Grossberg delayed neural networks by addressing a challenge namely stability of sets. Such extended concept is of considerable interest to numerous systems capable of approaching not only one equilibrium state. Results on uniform global asymptotic stability and uniform global exponential stability with respect to sets for the model under consideration are established. The main tools are expansions of the Lyapunov method and the comparison principle. In addition, the obtained results for the uncertain case contributed to the development of the stability theory of uncertain reaction-diffusion Cohen-Grossberg delayed neural networks and their applications. Moreover, examples are given to demonstrate the feasibility of our results.

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