Synchronization of spatiotemporal networks via backstepping using neighbor information

A backstepping scheme is proposed for synchronization between two complex dynamical networks with different structures. The nodes of the networks are spatiotemporal chaotic systems. A recurrence relation containing the information from neighbors is established so that only one control input is needed to synchronize two spatiotemporal networks. The Lyapunov stability theory is applied to prove that the differences between the drive and response networks tend to zero asymptotically under the control. The proposed scheme is numerically implemented in the synchronization of two networks with the Fisher–Kolmogorov and the Burgers spatiotemporal chaotic systems as the nodes.

[1]  Zidong Wang,et al.  Global Synchronization for Discrete-Time Stochastic Complex Networks With Randomly Occurred Nonlinearities and Mixed Time Delays , 2010, IEEE Transactions on Neural Networks.

[2]  Ligang Wu,et al.  Sliding mode control with bounded L2 gain performance of Markovian jump singular time-delay systems , 2012, Autom..

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

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

[5]  Chengren Li,et al.  Projective synchronization of the small-world delayed network with uncertainty , 2014 .

[6]  Gang Feng,et al.  Robust controller design of a class of nonlinear time delay systems via backstepping method , 2008, Autom..

[7]  A. P. Misra,et al.  Synchronization of spatiotemporal semiconductor lasers and its application in color image encryption , 2011, 1102.2775.

[8]  Young-Bum Kim,et al.  Corrigendum: Clusterin and LRP2 are critical components of the hypothalamic feeding regulatory pathway , 2013 .

[9]  Chee Seng Chan,et al.  Robust synchronization of uncertain chaotic neural networks with randomly occurring uncertainties and non-fragile output coupling delayed feedback controllers , 2014, Nonlinear Dynamics.

[10]  Ling Lü,et al.  Synchronization of spatiotemporal chaos in complex networks via backstepping , 2012 .

[11]  J. Burgers.  A mathematical model illustrating the theory of turbulence , 1948 .

[12]  R. Fisher.  THE USE OF MULTIPLE MEASUREMENTS IN TAXONOMIC PROBLEMS , 1936 .

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

[14]  Xikui Ma,et al.  Synchronization control of cross-strict feedback hyperchaotic system based on cross active backstepping design , 2007 .

[15]  Jinde Cao,et al.  Synchronization of hybrid-coupled heterogeneous networks: Pinning control and impulsive control schemes , 2014, J. Frankl. Inst..

[16]  Yongguang Yu,et al.  Adaptive hybrid projective synchronization of uncertain chaotic systems based on backstepping design , 2011 .

[17]  S. C. Tong,et al.  Adaptive Neural Network Decentralized Backstepping Output-Feedback Control for Nonlinear Large-Scale Systems With Time Delays , 2011, IEEE Transactions on Neural Networks.

[18]  M. S. M. Noorani,et al.  Projective lag synchronization in drive-response dynamical networks with delay coupling via hybrid feedback control , 2014, Nonlinear Dynamics.

[19]  R. Khordad,et al.  ADAPTIVE SYNCHRONIZATION OF TWO CHAOTIC CHEN SYSTEMS WITH UNKNOWN PARAMETERS , 2014 .

[20]  J. Kurths,et al.  Outer synchronization of coupled discrete-time networks. , 2009, Chaos.

[21]  Guodong Zhang,et al.  Global anti-synchronization of a class of chaotic memristive neural networks with time-varying delays , 2013, Neural Networks.

[22]  Ju H. Park,et al.  Robust adaptive backstepping synchronization for a class of uncertain chaotic systems using fuzzy disturbance observer , 2012 .

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