Adaptive Synchronization of Complex Dynamical Multilinks Networks with Similar Nodes

This paper studies the synchronization of complex dynamical networks with multilinks and similar nodes. The dynamics of all the nodes in the networks are impossible to be completely identical due to the differences of parameters or the existence of perturbations. Networks with similar nodes are universal in the real world. In order to depict the similarity of the similar nodes, we give the definition of the minimal similarity of the nodes in the network for the first time. We find the threshold of the minimal similarity of the nodes in the network. If the minimal similarity of the nodes is bigger than the threshold, then the similar nodes can achieve synchronization without controllers. Otherwise, adaptive synchronization method is adopted to synchronize similar nodes in the network. Some new synchronization criteria are proposed based on the Lyapunov stability theory. Finally, numerical simulations are given to illustrate the feasibility and the effectiveness of the proposed theoretical results.

[1]  Zengrong Liu,et al.  Exponential synchronization of complex networks with nonidentical time-delayed dynamical nodes , 2010 .

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

[3]  Wuneng Zhou,et al.  Structure identification and adaptive synchronization of uncertain general complex dynamical networks , 2009 .

[4]  Ming Li,et al.  On 1/f Noise , 2012 .

[5]  F. Garofalo,et al.  Controllability of complex networks via pinning. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Xiang Li,et al.  Pinning a complex dynamical network to its equilibrium , 2004, IEEE Trans. Circuits Syst. I Regul. Pap..

[7]  Jinde Cao,et al.  Synchronization of complex dynamical networks with nonidentical nodes , 2010 .

[8]  Guanrong Chen,et al.  Pinning control of scale-free dynamical networks , 2002 .

[9]  Wuneng Zhou,et al.  Adaptive synchronization of the complex dynamical network with non-derivative and derivative coupling , 2010 .

[10]  Wuneng Zhou,et al.  Adaptive lag synchronization and parameters adaptive lag identification of chaotic systems , 2010 .

[11]  Jinde Cao,et al.  Exponential Synchronization of Linearly Coupled Neural Networks With Impulsive Disturbances , 2011, IEEE Transactions on Neural Networks.

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

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

[14]  Wenwu Yu,et al.  On pinning synchronization of complex dynamical networks , 2009, Autom..

[15]  Ming Li,et al.  Representation of a Stochastic Traffic Bound , 2010, IEEE Transactions on Parallel and Distributed Systems.

[16]  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.

[17]  Haipeng Peng,et al.  Models and synchronization of time-delayed complex dynamical networks with multi-links based on adaptive control , 2010 .

[18]  Junan Lu,et al.  Pinning adaptive synchronization of a general complex dynamical network , 2008, Autom..

[19]  Frank L. Lewis,et al.  Distributed adaptive control for synchronization of unknown nonlinear networked systems , 2010, Autom..

[20]  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.

[21]  Ming Li,et al.  Quantitatively investigating the locally weak stationarity of modified multifractional Gaussian noise , 2012 .

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

[23]  Peng Shi,et al.  Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control , 2013 .

[24]  Zhirui Hu,et al.  Pinning adaptive synchronization of complex dynamical network with multi-links , 2012 .

[25]  Guanrong Chen,et al.  Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system , 2006 .

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

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

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