Asymptotic stability of stochastic reaction-diffusion delayed neural networks

2011 ◽  
Author(s):  
Shuman Pan ◽  
Lina Fu
Keyword(s):  
Neural Networks ◽  
Asymptotic Stability ◽  
Reaction Diffusion ◽  
Delayed Neural Networks ◽  
Stochastic Reaction

scholarly journals Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Li Wan ◽  
Qinghua Zhou ◽  
Jizi Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Ultimate Boundedness ◽  
Dynamical Behaviors ◽  
Weak Attractor ◽  
Stochastic Reaction ◽  
Theoretical Results

This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

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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