Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances

• Published in: IEEE transaction on neural networks and learning systems 2011-02, Vol.22 (2), p.329-336
• Main Authors: Jianquan Lu, Ho, D W C, Jinde Cao, Kurths, J
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Artificial Intelligence; Artificial neural networks; Computer science; control theory; systems; Computer Simulation - standards; Computer systems and distributed systems. User interface; Connectionism. Neural networks; Cortical Synchronization - physiology; Couplings; Delay; Desynchronizing impulses; Eigenvalues and eigenfunctions; Exact sciences and technology; globally exponential synchronization; Linear Models; linearly coupled neural networks; Mathematical Computing; Matrix decomposition; Neural networks; Neural Networks (Computer); Nonlinear Dynamics; Nonlinear dynamics and nonlinear dynamical systems; Physics; Signal Processing, Computer-Assisted; Software; Software Design; Statistical physics, thermodynamics, and nonlinear dynamical systems; Studies; Symmetric matrices; Synchronization; Synchronization; coupled oscillators; Time Factors
• ISSN: 1045-9227; 2162-237X; 1941-0093; 2162-2388
• DOI: 10.1109/TNN.2010.2101081

This brief investigates globally exponential synchronization for linearly coupled neural networks (NNs) with time-varying delay and impulsive disturbances. Since the impulsive effects discussed in this brief are regarded as disturbances, the impulses should not happen too frequently. The concept of average impulsive interval is used to formalize this phenomenon. By referring to an impulsive delay differential inequality, we investigate the globally exponential synchronization of linearly coupled NNs with impulsive disturbances. The derived sufficient condition is closely related with the time delay, impulse strengths, average impulsive interval, and coupling structure of the systems. The obtained criterion is given in terms of an algebraic inequality which is easy to be verified, and hence our result is valid for large-scale systems. The results extend and improve upon earlier work. As a numerical example, a small-world network composing of impulsive coupled chaotic delayed NN nodes is given to illustrate our theoretical result.