Projective and lag synchronization between general complex networks via impulsive control

This paper mainly investigates the projective and lag synchronization between general complex networks via impulsive control. A general drive complex network and an impulsively controlled slave network are presented in the model. Specially, the coupling matrix in this model is not assumed to be symmetric, diffusive or irreducible. Some criteria and corollaries are, respectively, derived for the projective synchronization and lag synchronization between the presented impulsively controlled complex networks. Finally, the results are illustrated by complex networks composed of the chaotic Lorenz systems. All the numerical simulations verify the correctness of the theoretical results.

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

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

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

[4]  Beom Jun Kim,et al.  Synchronization on small-world networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[6]  Guanrong Chen,et al.  Dynamics of periodic delayed neural networks , 2004, Neural Networks.

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

[8]  Gang Feng,et al.  Controlling complex dynamical networks with coupling delays to a desired orbit , 2006 .

[9]  Guanrong Chen,et al.  Global synchronization and asymptotic stability of complex dynamical networks , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[10]  Tianping Chen,et al.  Robust synchronization of delayed neural networks based on adaptive control and parameters identification , 2006 .

[11]  Jürgen Kurths,et al.  Synchronization between two coupled complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  Jun-an Lu,et al.  Topology identification of weighted complex dynamical networks , 2007 .

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

[14]  Jinde Cao,et al.  Adaptive synchronization of uncertain dynamical networks with delayed coupling , 2008 .

[15]  Yongqing Yang,et al.  The impulsive control synchronization of the drive-response complex system☆ , 2008 .

[16]  Jin Zhou,et al.  Exponential Stability of Impulsive Delayed Linear Differential Equations , 2009, IEEE Transactions on Circuits and Systems II: Express Briefs.

[17]  Wenwu Yu,et al.  Identifying the Topology of a Coupled FitzHugh–Nagumo Neurobiological Network via a Pinning Mechanism , 2009, IEEE Transactions on Neural Networks.

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

[19]  Xingyuan Wang,et al.  Projective synchronization of nonlinear-coupled spatiotemporal chaotic systems , 2010 .

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

[21]  Linying Xiang,et al.  On pinning synchronization of general coupled networks , 2011 .

[22]  Mohammad Pourmahmood Aghababa.  Comments on “Adaptive synchronization of fractional-order chaotic systems via a single driving variable” [Nonlinear Dyn. (2011), doi:10.1007/s11071-011-9944-2] , 2011 .

[23]  G. Mahmoud,et al.  Lag synchronization of hyperchaotic complex nonlinear systems , 2012 .

[24]  Meng Liu,et al.  Adaptive projective synchronization of dynamical networks with distributed time delays , 2012 .