Finite-Time Synchronization of Complex Dynamical Networks with Time-Varying Delays and Nonidentical Nodes

In this paper, we investigated the finite-time synchronization (FTS) problem for a class of time-delayed complex networks with nonidentical nodes onto any uniformly smooth state. By employing the finite-time stability theorem and designing two types of novel controllers, we obtained some simple sufficient conditions for the FTS of addressed complex networks. Furthermore, we also analyzed the effects of control variables on synchronization performance. Finally, we showed the effectiveness and feasibility of our methods by giving two numerical examples.

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

[2]  Jinde Cao,et al.  Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects , 2007 .

[3]  Zhidong Teng,et al.  Finite-time synchronization for memristor-based neural networks with time-varying delays , 2015, Neural Networks.

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

[5]  Zhidong Teng,et al.  Lag synchronization for Cohen–Grossberg neural networks with mixed time-delays via periodically intermittent control , 2017, Int. J. Comput. Math..

[6]  Hongtao Lu,et al.  Cluster synchronization in the adaptive complex dynamical networks via a novel approach , 2011 .

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

[8]  Lihong Huang,et al.  Synchronization analysis of delayed complex networks via adaptive time-varying coupling strengths , 2009 .

[9]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[10]  Jinde Cao,et al.  Fixed-time synchronization of delayed memristor-based recurrent neural networks , 2017, Science China Information Sciences.

[11]  Guanrong Chen,et al.  Complex networks: small-world, scale-free and beyond , 2003 .

[12]  Z. Duan,et al.  Network synchronizability analysis: a graph-theoretic approach. , 2008, Chaos.

[13]  Zhi Li,et al.  New eigenvalue based approach to synchronization in asymmetrically coupled networks. , 2007, Chaos.

[14]  Song Zheng,et al.  Adaptive synchronization of two nonlinearly coupled complex dynamical networks with delayed coupling , 2012 .

[15]  WU Ran-chao Impulsive Control and Synchronization of a New Chaotic System , 2009 .

[16]  M. P. Aghababa,et al.  Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique , 2011 .

[17]  S H Strogatz,et al.  Coupled oscillators and biological synchronization. , 1993, Scientific American.

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

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

[20]  Jinde Cao,et al.  Adaptive synchronization of neural networks with or without time-varying delay. , 2006, Chaos.

[21]  Jinde Cao,et al.  Generalized synchronization for delayed chaotic neural networks: a novel coupling scheme , 2006 .

[22]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[23]  Yigang He,et al.  Finite-Time Synchronization of a Class of Second-Order Nonlinear Multi-Agent Systems Using Output Feedback Control , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[24]  Luo Runzi,et al.  Impulsive control and synchronization of a new chaotic system , 2008 .

[25]  Tianping Chen,et al.  New approach to synchronization analysis of linearly coupled ordinary differential systems , 2006 .

[26]  Jinde Cao,et al.  Finite-time synchronisation control of complex networks via non-smooth analysis , 2015 .

[27]  Zengrong Liu,et al.  Periodically intermittent controlling complex dynamical networks with time-varying delays to a desired orbit , 2009 .

[28]  Song Zheng,et al.  Adaptive projective synchronization in complex networks with time-varying coupling delay , 2009 .

[29]  Zhidong Teng,et al.  Finite-time synchronization for fuzzy cellular neural networks with time-varying delays , 2016, Fuzzy Sets Syst..

[30]  V. P ez-Villar,et al.  Autowaves for Image Processing on a Two-Dimensional CNN Array of Excitable Nonlinear Circuits: Flat and Wrinkled Labyrinths V. Perez-Mufiuzuri, V. Perez-Villar, and Leon 0. Chua, Fellow, ZEEE , 1993 .

[31]  Chunyu Yang,et al.  Robust finite-time stability and stabilization of uncertain Markovian jump systems with time-varying delay , 2017, Appl. Math. Comput..

[32]  Wei Zhang,et al.  Finite-time chaos control via nonsingular terminal sliding mode control , 2009 .

[33]  Jinde Cao,et al.  Finite-time synchronization of fractional-order memristor-based neural networks with time delays , 2016, Neural Networks.

[34]  Zhaoyan Wu,et al.  FINITE-TIME SYNCHRONIZATION OF DYNAMICAL NETWORKS COUPLED WITH COMPLEX-VARIABLE CHAOTIC SYSTEMS , 2013 .

[35]  Zhang Yifeng,et al.  A secure communication scheme based on cellular neural network , 1997, 1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335).

[36]  Daoyi Xu,et al.  Stability Analysis and Design of Impulsive Control Systems With Time Delay , 2007, IEEE Transactions on Automatic Control.

[37]  L. Chua,et al.  Synchronization in an array of linearly coupled dynamical systems , 1995 .

[38]  Jinde Cao,et al.  Finite-time generalized synchronization of nonidentical delayed chaotic systems , 2016 .

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

[40]  Jinde Cao,et al.  Nonsmooth finite-time stabilization of neural networks with discontinuous activations , 2014, Neural Networks.

[41]  Zhidong Teng,et al.  Synchronization of complex community networks with nonidentical nodes and adaptive coupling strength , 2011 .

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

[43]  Jinde Cao,et al.  Finite-time stochastic synchronization of complex networks , 2010 .

[44]  Bin Wang,et al.  Finite-time synchronization control of complex dynamical networks with time delay , 2013, Commun. Nonlinear Sci. Numer. Simul..

[45]  Mohammad Pourmahmood Aghababa,et al.  Finite-time stabilization of a non-autonomous chaotic rotating mechanical system , 2012, J. Frankl. Inst..