Impulsive synchronization of stochastic reaction–diffusion neural networks with mixed time delays

2018 ◽  
Vol 103 ◽  
pp. 83-93 ◽  
Author(s):  
Yin Sheng ◽  
Zhigang Zeng
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Reaction Diffusion ◽  
Mixed Time Delays ◽  
Impulsive Synchronization ◽  
Stochastic Reaction

scholarly journals Stability Analysis for Impulsive Stochastic Reaction-Diffusion Differential System and Its Application to Neural Networks

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Yanke Du ◽  
Yanlu Li ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Differential System ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Impulsive Effects ◽  
Stability Criteria ◽  
Mixed Time Delays ◽  
The Stability ◽  
Stochastic Reaction

This paper is concerned with the stability of impulsive stochastic reaction-diffusion differential systems with mixed time delays. First, an equivalent relation between the solution of a stochastic reaction-diffusion differential system with time delays and impulsive effects and that of corresponding system without impulses is established. Then, some stability criteria for the stochastic reaction-diffusion differential system with time delays and impulsive effects are derived. Finally, the stability criteria are applied to impulsive stochastic reaction-diffusion Cohen-Grossberg neural networks with mixed time delays, and sufficient conditions are obtained for the exponentialp-stability of the zero solution to the neural networks. An example is given to illustrate the effectiveness of our theoretical results. The systems we studied in this paper are more general, and some existing results are improved and extended.

scholarly journals Dynamical Behaviors of Impulsive Stochastic Reaction-Diffusion Neural Networks with Mixed Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Weiyuan Zhang ◽  
Junmin Li ◽  
Minglai Chen
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Linear Matrix ◽  
Mixed Time Delays ◽  
Dynamical Behaviors ◽  
Proposed Model ◽  
The Mean ◽  
Stochastic Reaction

We discuss the dynamical behaviors of impulsive stochastic reaction-diffusion neural networks (ISRDNNs) with mixed time delays. By using a well-knownL-operator differential inequality with mixed time delays and combining with the Lyapunov-Krasovkii functional approach, as well as linear matrix inequality (LMI) technique, some novel sufficient conditions are derived to ensure the existence, uniqueness, and global exponential stability of the periodic solutions for ISRDNNs with mixed time delays in the mean square sense. The obtained sufficient conditions depend on the reaction-diffusion terms. The results of this paper are new and improve some of the previously known results. The proposed model is quite general since many factors such as noise perturbations, impulsive phenomena, and mixed time delays are considered. Finally, two numerical examples are provided to verify the usefulness of the obtained results.

scholarly journals Stability Analysis for Stochastic Markovian Jump Reaction-Diffusion Neural Networks with Partially Known Transition Probabilities and Mixed Time Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-17 ◽  
Author(s):  
Weiyuan Zhang ◽  
Junmin Li ◽  
Naizheng Shi
Keyword(s):  
Neural Networks ◽  
Time Delays ◽  
Partial Information ◽  
Transition Probabilities ◽  
Transition Probability ◽  
Reaction Diffusion ◽  
Stability Conditions ◽  
Markovian Jump ◽  
Mixed Time Delays ◽  
The Stability

The stability problem is proposed for a new class of stochastic Markovian jump reaction-diffusion neural networks with partial information on transition probability and mixed time delays. The new stability conditions are established in terms of linear matrix inequalities (LMIs). To reduce the conservatism of the stability conditions, an improved Lyapunov-Krasovskii functional and free-connection weighting matrices are introduced. The obtained results are dependent on delays and the measure of the space AND, therefore, have less conservativeness than delay-independent and space-independent ones. An example is given to show the effectiveness of the obtained results.

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