Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances

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.

[1]  Huijun Gao,et al.  Asynchronously switched control of switched linear systems with average dwell time , 2010, Autom..

[2]  Gang Zhang,et al.  Synchronization of complex dynamical networks via impulsive control. , 2007, Chaos.

[3]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[4]  Yan-Wu Wang,et al.  Robust Stabilization of Complex Switched Networks With Parametric Uncertainties and Delays Via Impulsive Control , 2009, IEEE Transactions on Circuits and Systems I: Regular Papers.

[5]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[6]  Chunguang Li,et al.  Synchronization in general complex dynamical networks with coupling delays , 2004 .

[7]  Jürgen Kurths,et al.  Consensus over directed static networks with arbitrary finite communication delays. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  David J. Hill,et al.  A Hybrid impulsive and Switching Control Strategy for Synchronization of Nonlinear Systems and Application to Chua's Chaotic Circuit , 2006, Int. J. Bifurc. Chaos.

[9]  Chai Wah Wu,et al.  Synchronization in Complex Networks of Nonlinear Dynamical Systems , 2008 .

[10]  D. Baĭnov,et al.  Systems with impulse effect : stability, theory, and applications , 1989 .

[11]  Zhi-Hong Guan,et al.  On synchronization of hybrid switching and impulsive networks , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[12]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[13]  A. Morse,et al.  Stability of switched systems with average dwell-time , 1999, Proceedings of the 38th IEEE Conference on Decision and Control (Cat. No.99CH36304).

[14]  Jinde Cao,et al.  Robust impulsive synchronization of coupled delayed neural networks with uncertainties , 2007 .

[15]  Ligang Wu,et al.  Exponential stabilization of switched stochastic dynamical networks , 2009 .

[16]  Wei Wu,et al.  Global Synchronization Criteria of Linearly Coupled Neural Network Systems With Time-Varying Coupling , 2008, IEEE Transactions on Neural Networks.

[17]  Daniel W. C. Ho,et al.  Pinning Stabilization of Linearly Coupled Stochastic Neural Networks via Minimum Number of Controllers , 2009, IEEE Transactions on Neural Networks.

[18]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[19]  Jin Zhou,et al.  Synchronization in complex delayed dynamical networks with impulsive effects , 2007 .

[20]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .

[21]  David J. Hill,et al.  Robust stability of complex impulsive dynamical systems , 2007, 2007 46th IEEE Conference on Decision and Control.

[22]  Daoyi Xu,et al.  Stability Analysis of Delay Neural Networks With Impulsive Effects , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[23]  J. Kurths,et al.  Detecting phase synchronization by localized maps: Application to neural networks , 2007, 0706.3317.

[24]  C. Wu.  Synchronization in networks of nonlinear dynamical systems coupled via a directed graph , 2005 .

[25]  J. Liang,et al.  Robust Synchronization of an Array of Coupled Stochastic Discrete-Time Delayed Neural Networks , 2008, IEEE Transactions on Neural Networks.

[26]  D. Ho,et al.  Local and global synchronization in general complex dynamical networks with delay coupling , 2008 .

[27]  JIANQUAN LU,et al.  Synchronization in an Array of Nonlinearly Coupled Chaotic Neural Networks with Delay Coupling , 2008, Int. J. Bifurc. Chaos.

[28]  M. Gilli.  Strange attractors in delayed cellular neural networks , 1993 .

[29]  Ingo Fischer,et al.  Synchronization of chaotic semiconductor laser dynamics on subnanosecond time scales and its potential for chaos communication , 2000 .

[30]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2005, IEEE Transactions on Automatic Control.

[31]  M. Newman,et al.  Scaling and percolation in the small-world network model. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Tao Yang,et al.  Impulsive Systems and Control: Theory and Applications , 2001 .

[33]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[34]  Xuemin Shen,et al.  On hybrid impulsive and switching systems and application to nonlinear control , 2005, IEEE Transactions on Automatic Control.

[35]  Frank C. Hoppensteadt,et al.  Pattern recognition via synchronization in phase-locked loop neural networks , 2000, IEEE Trans. Neural Networks Learn. Syst..

[36]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[37]  Daniel W. C. Ho,et al.  Globally Exponential Synchronization and Synchronizability for General Dynamical Networks , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[38]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[39]  Guanrong Chen,et al.  New criteria for synchronization stability of general complex dynamical networks with coupling delays , 2006 .

[40]  Xinzhi Liu,et al.  Robust impulsive synchronization of uncertain dynamical networks , 2005, IEEE Transactions on Circuits and Systems I: Regular Papers.

[41]  Daniel Liberzon,et al.  Switching in Systems and Control , 2003, Systems & Control: Foundations & Applications.