Synchronization of impulsively coupled complex systems with delay.

This paper investigates the synchronization of complex systems with delay that are impulsively coupled at discrete instants only. Based on the comparison theorem of impulsive differential system, a distributed impulsive control scheme is proposed to achieve the synchronization for systems with delay. In the control strategy, the influence of all nodes to network synchronization relies on its weight. The proposed control scheme is applied to the chaotic delayed Hopfield neural networks and numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.

[1]  C. K. Michael Tse,et al.  Adaptive Feedback Synchronization of a General Complex Dynamical Network With Delayed Nodes , 2008, IEEE Transactions on Circuits and Systems II: Express Briefs.

[2]  Konrad Campowsky,et al.  BonFIRE: A Multi-cloud Test Facility for Internet of Services Experimentation , 2012, TRIDENTCOM.

[3]  Gang Feng,et al.  Synchronization of Complex Dynamical Networks With Time-Varying Delays Via Impulsive Distributed Control , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

[4]  Zengrong Liu,et al.  Robust impulsive synchronization of complex delayed dynamical networks , 2008 .

[5]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[6]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[7]  Mingzhou Ding,et al.  Enhancement of neural synchrony by time delay. , 2004, Physical review letters.

[8]  Xiaofeng Liao,et al.  Impulsive synchronization of nonlinear coupled chaotic systems , 2004 .

[9]  Junan Lu,et al.  Synchronization of impulsively Coupled Systems , 2008, Int. J. Bifurc. Chaos.

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

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

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

[13]  Haibo Jiang,et al.  Impulsive synchronization of networked nonlinear dynamical systems , 2010 .

[14]  S. Strogatz.  Exploring complex networks , 2001, Nature.

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

[16]  Jiang-Wen Xiao,et al.  Impulsive control for synchronization of a class of continuous systems. , 2004, Chaos.

[17]  Guanrong Chen,et al.  Chaos synchronization of general complex dynamical networks , 2004 .

[18]  Guanrong Chen,et al.  A time-varying complex dynamical network model and its controlled synchronization criteria , 2004, IEEE Trans. Autom. Control..

[19]  Tianping Chen,et al.  Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix , 2008 .

[20]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[21]  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.

[22]  Haibo Jiang,et al.  Consensus of multi-agent linear dynamic systems via impulsive control protocols , 2011, Int. J. Syst. Sci..

[23]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Xiaofeng Liao,et al.  Impulsive synchronization of chaotic systems. , 2005, Chaos.

[25]  Yang Tao,et al.  Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication , 1997 .

[26]  T. Carroll,et al.  Master Stability Functions for Synchronized Coupled Systems , 1998 .

[27]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

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

[29]  Yinping Zhang,et al.  Impulsive robust fault-tolerant feedback control for chaotic Lur'e systems , 2009 .

[30]  Jitao Sun,et al.  Impulsive control of Rössler systems , 2003 .

[31]  Jinde Cao,et al.  New communication schemes based on adaptive synchronization. , 2007, Chaos.

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

[33]  Tianping Chen,et al.  Synchronization analysis of linearly coupled systems described by differential equations with a coupling delay , 2006 .

[34]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[35]  Jinde Cao,et al.  Exponential synchronization of the complex dynamical networks with a coupling delay and impulsive effects , 2010 .

[36]  M. Hasler,et al.  Connection Graph Stability Method for Synchronized Coupled Chaotic Systems , 2004 .

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