Pinning Synchronization of Complex Dynamical Networks on Time Scales

The purpose of this paper is to investigate the synchronization problem of complex dynamical networks on time scales, which includes the synchronization problem of continuous-time and discrete-time complex dynamical networks as special cases. A pinning control strategy is designed to achieve synchronization of complex dynamical networks on time scales. Based on the theory of calculus on time scales and the Lyapunov method, pinning synchronization criteria for complex dynamical networks on time scales are established. Moreover, a numerical example is given to verify the effectiveness of theoretical results.

[1]  Ranran Cheng,et al.  Pinning synchronization of discrete dynamical networks with delay coupling , 2016 .

[2]  Guanrong Chen,et al.  Pinning control and synchronization on complex dynamical networks , 2014, International Journal of Control, Automation and Systems.

[3]  Tingwen Huang,et al.  Global exponential synchronization of nonautonomous recurrent neural networks with time delays on time scales , 2018, Appl. Math. Comput..

[4]  Linying Xiang,et al.  Pinning control of complex dynamical networks with general topology , 2007 .

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

[6]  Shan Gao,et al.  Global Exponential Stability for Impulsive BAM Neural Networks with Distributed Delays on Time Scales , 2010, Neural Processing Letters.

[7]  M. Syed Ali,et al.  Synchronization Criterion of Complex Dynamical Networks with Both Leakage Delay and Coupling Delay on Time Scales , 2018, Neural Processing Letters.

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

[9]  P. Maher,et al.  Handbook of Matrices , 1999, The Mathematical Gazette.

[10]  Jinde Cao,et al.  Global synchronization of complex networks with discrete time delays and stochastic disturbances , 2011, Neural Computing and Applications.

[11]  Xiaodong Lu,et al.  Finite-time synchronization of nonlinear complex dynamical networks on time scales via pinning impulsive control , 2018, Neurocomputing.

[12]  Jinde Cao,et al.  Synchronization of complex dynamical networks with discrete time delays on time scales , 2015, Neurocomputing.

[13]  M. Syed Ali,et al.  Event Triggered Finite Time H∞\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H_{\infty }$$\end{document} Boundedness , 2018, Neural Processing Letters.

[14]  M. Bohner,et al.  Global Stability of Complex-Valued Neural Networks on Time Scales , 2011 .

[15]  Frank L. Lewis,et al.  Event-Based Time-Interval Pinning Control for Complex Networks on Time Scales and Applications , 2018, IEEE Transactions on Industrial Electronics.

[16]  Guanrong Chen,et al.  Synchronization and desynchronization of complex dynamical networks: an engineering viewpoint , 2003 .

[17]  A. Peterson,et al.  Advances in Dynamic Equations on Time Scales , 2012 .

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

[19]  W. Stewart,et al.  The Kronecker product and stochastic automata networks , 2004 .

[20]  Jinde Cao,et al.  Hilger-type impulsive differential inequality and its application to impulsive synchronization of delayed complex networks on time scales , 2018, Science China Information Sciences.

[21]  Tianping Chen,et al.  Synchronization analysis of linearly coupled networks of discrete time systems , 2004 .

[22]  Anping Chen,et al.  Global exponential stability of delayed BAM network on time scale , 2008, Neurocomputing.

[23]  A. Peterson,et al.  Dynamic Equations on Time Scales: An Introduction with Applications , 2001 .

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

[25]  FaloutsosMichalis,et al.  On power-law relationships of the Internet topology , 1999 .

[26]  Xiaodong Lu,et al.  Synchronization of complex dynamical networks on time scales via Wirtinger-based inequality , 2016, Neurocomputing.

[27]  M. Syed Ali,et al.  Synchronization of complex dynamical networks with hybrid coupling delays on time scales by handling multitude Kronecker product terms , 2016, Appl. Math. Comput..

[28]  Kexue Zhang,et al.  Synchronization of linear dynamical networks on time scales: Pinning control via delayed impulses , 2016, Autom..

[29]  Tianping Chen,et al.  Pinning Complex Networks by a Single Controller , 2007, IEEE Transactions on Circuits and Systems I: Regular Papers.

[30]  Xinchu Fu,et al.  On pinning control of some typical discrete-time dynamical networks , 2010 .

[31]  Michalis Faloutsos,et al.  On power-law relationships of the Internet topology , 1999, SIGCOMM '99.

[32]  Jürgen Kurths,et al.  Synchronization of complex dynamical networks with time delays , 2006 .

[33]  Aleksey Ogulenko.  Asymptotical properties of social network dynamics on time scales , 2017, J. Comput. Appl. Math..

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

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

[36]  Zhaoyan Wu.  Synchronization of discrete dynamical networks with non-delayed and delayed coupling , 2015, Appl. Math. Comput..

[37]  Jinde Cao,et al.  On Pinning Synchronization of Directed and Undirected Complex Dynamical Networks , 2010, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[39]  A. Peterson,et al.  Dynamic Equations on Time Scales , 2001 .