Pinning synchronization of spatial diffusion coupled reaction-diffusion neural networks with and without multiple time-varying delays

2017 ◽  
Vol 227 ◽  
pp. 92-100 ◽  
Author(s):  
Shu-Xue Wang ◽  
Yan-Li Huang ◽  
Bei-Bei Xu
Keyword(s):  
Neural Networks ◽  
Reaction Diffusion ◽  
Spatial Diffusion ◽  
Multiple Time ◽  
Time Varying ◽  
Coupled Reaction

scholarly journals Stochastic Synchronization of Reaction-Diffusion Neural Networks under General Impulsive Controller with Mixed Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Xinsong Yang ◽  
Chuangxia Huang ◽  
Zhichun Yang
Keyword(s):  
Neural Networks ◽  
Control Method ◽  
Mathematical Proof ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Distributed Delays ◽  
Mixed Delays ◽  
Multiple Time ◽  
Time Varying ◽  
Stochastic Perturbations

This paper investigates drive-response synchronization of a class of reaction-diffusion neural networks with time-varying discrete and distributed delays via general impulsive control method. Stochastic perturbations in the response system are also considered. The impulsive controller is assumed to be nonlinear and has multiple time-varying discrete and distributed delays. Compared with existing nondelayed impulsive controller, this general impulsive controller is more practical and essentially important since time delays are unavoidable in practical operation. Based on a novel impulsive differential inequality, the properties of random variables and Lyapunov functional method, sufficient conditions guaranteeing the global exponential synchronization in mean square are derived through strict mathematical proof. In our synchronization criteria, the distributed delays in both continuous equation and impulsive controller play important role. Finally, numerical simulations are given to show the effectiveness of the theoretical results.

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