Fixed point and p-stability of T–S fuzzy impulsive reaction–diffusion dynamic neural networks with distributed delay via Laplacian semigroup

2019 ◽  
Vol 335 ◽  
pp. 170-184 ◽  
Author(s):  
Ruofeng Rao ◽  
Shouming Zhong ◽  
Zhilin Pu
Keyword(s):  
Neural Networks ◽  
Fixed Point ◽  
Distributed Delay ◽  
Reaction Diffusion ◽  
Dynamic Neural Networks ◽  
Impulsive Reaction

scholarly journals Stability Analysis of Impulsive Stochastic Reaction-Diffusion Cellular Neural Network with Distributed Delay via Fixed Point Theory

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Ruofeng Rao ◽  
Shouming Zhong
Keyword(s):  
Fixed Point ◽  
Fixed Point Theory ◽  
Distributed Delay ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
Point Theory ◽  
Complete Space ◽  
Practical Engineering ◽  
The Fixed Point Theorem ◽  
The Stability

This paper investigates the stochastically exponential stability of reaction-diffusion impulsive stochastic cellular neural networks (CNN). The reaction-diffusion pulse stochastic system model characterizes the complexity of practical engineering and brings about mathematical difficulties, too. However, the difficulties have been overcome by constructing a new contraction mapping and an appropriate distance on a product space which is guaranteed to be a complete space. This is the first time to employ the fixed point theorem to derive the stability criterion of reaction-diffusion impulsive stochastic CNN with distributed time delays. Finally, an example is provided to illustrate the effectiveness of the proposed methods.

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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