Exponential synchronization in complex networks with a single coupling delay

Abstract This paper investigates local exponential synchronization of a general complex network with a single coupling delay. The coupling matrix and time delay in such a network are both time varying. According to the existence of the invariant synchronization manifold, we study the synchronization issues of the concerned network with k -type and non- k -type topologies, respectively. Several delay-dependent synchronization criteria for arbitrary delayed networks are derived in form of lower dimensional linear matrix inequalities by means of Lyapunov function approach. By solving the matrix inequalities, it is shown that, no matter what topology of the delayed network is, there exists a threshold of delay below which, synchronization is achieved. The effectiveness of our results is illustrated with numerical simulations in the end.

[1]  Tianping Chen,et al.  Synchronization in general complex delayed dynamical networks , 2006, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[3]  Jun Zhao,et al.  Stability of dynamical networks with non-identical nodes: A multiple v-Lyapunov function method , 2011, Autom..

[4]  A. Jadbabaie,et al.  Effects of Delay in Multi-Agent Consensus and Oscillator Synchronization , 2010, IEEE Transactions on Automatic Control.

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

[6]  Jianye Zhao,et al.  Enhancing consensus in weighted networks with coupling time-delay , 2012 .

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

[8]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[9]  Jinde Cao,et al.  Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying Delay , 2008, SIAM J. Appl. Dyn. Syst..

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

[11]  Guanrong Chen,et al.  Global Robust Stability and Synchronization of Networks With Lorenz-Type Nodes , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[13]  L. Kocarev,et al.  Towards generalized synchronization of strictly different chaotic systems [rapid communication] , 2005 .

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

[15]  K. Aihara,et al.  Synchronization of coupled nonidentical genetic oscillators , 2006, Physical biology.

[16]  L. Jiao,et al.  Synchronization in complex delayed dynamical networks with nonsymmetric coupling , 2007 .

[17]  Yingmin Jia,et al.  Distributed robust Hinfinity consensus control in directed networks of agents with time-delay , 2008, Syst. Control. Lett..

[18]  Yiguang Liu,et al.  Global synchronization for directed complex networks , 2010 .

[19]  S. Strogatz,et al.  Synchronization of pulse-coupled biological oscillators , 1990 .

[20]  Carroll,et al.  Synchronization in chaotic systems. , 1990, Physical review letters.

[21]  Hongtao Lu,et al.  Exponential synchronization of weighted general delay coupled and non-delay coupled dynamical networks , 2010, Comput. Math. Appl..

[22]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[23]  Hong-yong Yang,et al.  Chaos Synchronization of General Complex Dynamical Networks with Coupling Delays , 2006, 2006 6th World Congress on Intelligent Control and Automation.

[24]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[25]  Mario di Bernardo,et al.  Contraction Theory and Master Stability Function: Linking Two Approaches to Study Synchronization of Complex Networks , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[26]  Xiaofan Wang,et al.  On synchronization in scale-free dynamical networks , 2005 .

[27]  J. Kurths,et al.  Synchronization in Oscillatory Networks , 2007 .

[28]  K. Gopalsamy.  Stability and Oscillations in Delay Differential Equations of Population Dynamics , 1992 .

[29]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[30]  M. Hasler,et al.  Synchronization in asymmetrically coupled networks with node balance. , 2006, Chaos.

[31]  Jürgen Jost,et al.  Delays, connection topology, and synchronization of coupled chaotic maps. , 2004, Physical review letters.

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

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

[34]  Cristina Masoller,et al.  Complex transitions to synchronization in delay-coupled networks of logistic maps , 2011, 1105.5784.

[35]  Jinde Cao,et al.  Global synchronization in arrays of delayed neural networks with constant and delayed coupling , 2006 .

[36]  Jun Zhao,et al.  Synchronization of Dynamical Networks With Nonidentical Nodes: Criteria and Control , 2011, IEEE Transactions on Circuits and Systems I: Regular Papers.

[37]  Lei Wang,et al.  A general approach for synchronisation of nonlinear networked systems with switching topology , 2013, Int. J. Syst. Sci..

[38]  Chai Wah Wu,et al.  Synchronization in arrays of coupled nonlinear systems with delay and nonreciprocal time-varying coupling , 2005, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[40]  Alain Sarlette,et al.  Consensus Optimization on Manifolds , 2008, SIAM J. Control. Optim..

[41]  Lei Wang,et al.  Synchronization criteria for a generalized complex delayed dynamical network model , 2007 .

[42]  Jean-Jacques E. Slotine,et al.  On partial contraction analysis for coupled nonlinear oscillators , 2004, Biological Cybernetics.

[43]  Daizhan Cheng,et al.  Characterizing the synchronizability of small-world dynamical networks , 2004, IEEE Transactions on Circuits and Systems I: Regular Papers.