Synchronization for Time‐Delayed Coupling Complex Dynamic Networks with Different Dimensional Nodes Via Decentralized Dynamic Compensation Controllers

The objective of this paper is to investigate the synchronization for nonlinear time-delayed coupling complex dynamic networks with different dimensional nodes through the use of decentralized dynamic compensation controllers. We propose a nonlinear time-delayed coupling complex dynamic network model with similar nonlinear nodes, whose dimensions admit differences. For this kind of network model, based on Barbalat's lemma, decentralized dynamic compensation controllers are designed for the state synchronization of the coupled nodes under some mathematical conditions. In addition, the synchronization manifold is defined as an invariant manifold, which is regarded as the generalized case of the networks with the same node dynamics. Finally, numerical examples with chaotic and hyperchaotic nodes are presented to verify the effectiveness of our theoretical results.

[1]  Jinde Cao,et al.  Adaptive synchronization of uncertain coupled stochastic complex networks , 2011 .

[2]  Y.-H. Wang,et al.  Robust control for nonlinear similar composite systems with uncertain parameters , 2000 .

[3]  Yun Zhang,et al.  Stabilization and Synchronization of Complex Dynamical Networks With Different Dynamics of Nodes Via Decentralized Controllers , 2012, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[5]  C Masoller,et al.  Delay-induced synchronization phenomena in an array of globally coupled logistic maps. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Jun Zhao,et al.  Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes , 2009 .

[7]  Yun Zhang,et al.  The synchronization of complex dynamical networks with similar nodes and coupling time-delay , 2013, Appl. Math. Comput..

[8]  Tianping Chen,et al.  Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling , 2007 .

[9]  Ljupco Kocarev,et al.  Synchronization in power-law networks. , 2005, Chaos.

[10]  Lu Qi-Shao,et al.  A Criterion for Stability of Synchronization and Application to Coupled Chua's Systems , 2009 .

[11]  Shihua Chen,et al.  Global synchronization of nonlinearly coupled complex networks with non-delayed and delayed coupling , 2010 .

[12]  Georgi M. Dimirovski,et al.  Exponential synchronization of complex delayed dynamical networks with general topology , 2007, 2007 46th IEEE Conference on Decision and Control.

[13]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[14]  Huaguang Zhang,et al.  Synchronization stability in complex interconnected neural networks with nonsymmetric coupling , 2013, Neurocomputing.

[15]  Hongtao Lu,et al.  Hybrid synchronization of the general delayed and non-delayed complex dynamical networks via pinning control , 2012, Neurocomputing.

[16]  Zhong Chen,et al.  Impulsive synchronization of a general nonlinear coupled complex network , 2011 .

[17]  S. Wen,et al.  Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling , 2008 .

[18]  Song Zheng,et al.  A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays , 2012 .

[19]  Guanrong Chen,et al.  Synchronization in a class of weighted complex networks with coupling delays , 2008 .

[20]  Zengrong Liu,et al.  Impulsive synchronization seeking in general complex delayed dynamical networks , 2011 .

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

[22]  Mao-Yin Chen,et al.  Some Simple Synchronization Criteria for Complex Dynamical Networks , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

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

[24]  Shengyuan Xu,et al.  Delay‐dependent stability for Markovian genetic regulatory networks with time‐varying delays , 2012 .

[25]  Wang Li,et al.  Generalized outer synchronization between complex dynamical networks with time delay and noise perturbation , 2013, Commun. Nonlinear Sci. Numer. Simul..

[26]  Jun-An Lu,et al.  Delay-dependent synchronization in general complex delayed dynamical networks , 2009, Comput. Math. Appl..

[27]  Junmin Li,et al.  A new synchronization algorithm for delayed complex dynamical networks via adaptive control approach , 2012 .

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

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

[30]  Hongjie Li,et al.  Synchronization and state estimation for singular complex dynamical networks with time-varying delays , 2013, Commun. Nonlinear Sci. Numer. Simul..

[31]  M. G. Earl,et al.  Synchronization in oscillator networks with delayed coupling: a stability criterion. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[33]  Jin Zhou,et al.  Global synchronization in general complex delayed dynamical networks and its applications , 2007 .

[34]  Lihong Huang,et al.  Synchronization analysis of networks with both delayed and non-delayed couplings via adaptive pinning control method ☆ , 2010 .

[35]  Zhaosheng Feng,et al.  ESTIMATION OF DELAY ON SYNCHRONIZATION STABILITY IN A CLASS OF COMPLEX SYSTEMS WITH COUPLING DELAYS , 2008 .

[36]  Guanrong Chen,et al.  Novel criteria of synchronization stability in complex networks with coupling delays , 2007 .

[37]  Kestutis Pyragas.  SYNCHRONIZATION OF COUPLED TIME-DELAY SYSTEMS : ANALYTICAL ESTIMATIONS , 1998 .