Pinning Impulsive Synchronization of Reaction-Diffusion Neural Networks With Time-Varying Delays

• Published in: IEEE transaction on neural networks and learning systems Vol. 28; no. 5; pp. 1055 - 1067
• Main Authors: Liu, Xinzhi, Zhang, Kexue, Xie, Wei-Chau
• Format: Journal Article
• Language: English
• Published: United States IEEE 01.05.2017; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Adaptive systems; Biological neural networks; Boundary conditions; Delays; Diffusion; Dirichlet problem; Exponential synchronization; Heuristic algorithms; Lyapunov–Krasovskii functional; neural network; Neural networks; Neurons; Pinning; pinning impulsive control; reaction–diffusion; Synchronism; Synchronization; time delay
• ISSN: 2162-237X; 2162-2388
• DOI: 10.1109/TNNLS.2016.2518479

This paper investigates the exponential synchronization of reaction-diffusion neural networks with time-varying delays subject to Dirichlet boundary conditions. A novel type of pinning impulsive controllers is proposed to synchronize the reaction-diffusion neural networks with time-varying delays. By applying the Lyapunov functional method, sufficient verifiable conditions are constructed for the exponential synchronization of delayed reaction-diffusion neural networks with large and small delay sizes. It is shown that synchronization can be realized by pinning impulsive control of a small portion of neurons of the network; the technique used in this paper is also applicable to reaction-diffusion networks with Neumann boundary conditions. Numerical examples are presented to demonstrate the effectiveness of the theoretical results.