Global Exponential Synchronization of Nonlinearly Coupled Complex Dynamical Networks with Time-Varying Coupling Delays

This paper focuses on the global exponential synchronization problem of nonlinearly coupled complex dynamical networks with time-varying coupling delays. Several simple and generic global exponential synchronization criteria are derived based on the Lyapunov stability theory and the Dini derivatives using the Halanay and generalized Halanay inequalities. These criteria rely on system parameters alone and can be used conveniently in practical applications. In addition, the system parameters do not satisfy the conditions of the proposed criteria. That is, the system itself cannot synchronize. However, system synchronization can be achieved by adding the appropriate feedback controllers, thereby providing a practical and effective control method for complex dynamical networks. An estimation method of exponential convergence rate is also presented. Finally, the effectiveness of the proposed criteria is verified through numerical simulations.

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

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

[3]  Emilia Fridman,et al.  Passification-based decentralized adaptive synchronization of dynamical networks with time-varying delays , 2015, J. Frankl. Inst..

[4]  Zhidong Teng,et al.  Anti‐Synchronization and Intermittent Anti‐Synchronization of Two Identical Delay Hyperchaotic Chua Systems Via Linear Control , 2017 .

[5]  Hongtao Lu,et al.  Exponential synchronization of weighted general delay coupled and non-delay coupled dynamical networks , 2010, Comput. Math. Appl..

[6]  Xiao Fan Wang,et al.  Synchronization in scale-free dynamical networks: robustness and fragility , 2001, cond-mat/0105014.

[7]  Shuiming Cai,et al.  Outer synchronization between two hybrid-coupled delayed dynamical networks via aperiodically adaptive intermittent pinning control , 2016, Complex..

[8]  Jian-An Wang,et al.  Pinning lag synchronization of drive–response complex networks via intermittent control with two different switched periods , 2016 .

[9]  Ranran Cheng,et al.  Pinning synchronization of delayed complex dynamical networks with nonlinear coupling , 2014 .

[10]  Xiwei Liu,et al.  Cluster Synchronization in Directed Networks Via Intermittent Pinning Control , 2011, IEEE Transactions on Neural Networks.

[11]  H. Antosiewicz,et al.  Differential Equations: Stability, Oscillations, Time Lags , 1967 .

[12]  Zidong Wang,et al.  Synchronization and State Estimation for Discrete-Time Complex Networks With Distributed Delays , 2008, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[13]  Lucas Antiqueira,et al.  Analyzing and modeling real-world phenomena with complex networks: a survey of applications , 2007, 0711.3199.

[14]  Bao Cheng Li,et al.  Hybrid Synchronization of two complex delayed dynamical networks with nonidentical topologies and mixed coupling , 2016, Complex..

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

[16]  Liao Xiao,et al.  Globally Exponential Stability of Hopfield Neural Networks with Time varying Delays , 2000 .

[17]  Xiao Fan Wang,et al.  Synchronization in Small-World Dynamical Networks , 2002, Int. J. Bifurc. Chaos.

[18]  Ju H. Park,et al.  Guaranteed cost synchronization of a complex dynamical network via dynamic feedback control , 2012, Appl. Math. Comput..

[19]  Peipei Zhou,et al.  Synchronization analysis of hybrid-coupled delayed dynamical networks with impulsive effects: A unified synchronization criterion , 2015, J. Frankl. Inst..

[20]  Huaguang Zhang,et al.  Synchronization between two general complex networks with time-delay by adaptive periodically intermittent pinning control , 2014, Neurocomputing.

[21]  Song Zheng.  Synchronization analysis of complex-Variable chaotic systems with discontinuous unidirectional coupling , 2016, Complex..

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

[23]  Junan Lu,et al.  Adaptive synchronization of an uncertain complex dynamical network , 2006, IEEE Transactions on Automatic Control.

[24]  Reka Albert,et al.  Mean-field theory for scale-free random networks , 1999 .

[25]  T. Carroll,et al.  MASTER STABILITY FUNCTIONS FOR SYNCHRONIZED COUPLED SYSTEMS , 1999 .

[26]  Xinsong Yang,et al.  Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control , 2017, Appl. Math. Comput..

[27]  Tongchun Hu,et al.  Hybrid synchronization and parameter identification of uncertain interacted networks , 2016 .

[28]  Uchechukwu E. Vincent,et al.  Multi-switching combination synchronization of chaotic systems , 2015, Nonlinear Dynamics.

[29]  Georgi M. Dimirovski,et al.  Exponential synchronization of complex delayed dynamical networks with general topology , 2007, 2007 46th IEEE Conference on Decision and Control.

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

[31]  Daniel W. C. Ho,et al.  Partial-information-based synchronization analysis for complex dynamical networks , 2015, J. Frankl. Inst..

[32]  Mei Fang,et al.  Synchronization for complex dynamical networks with time delay and discrete-time information , 2015, Appl. Math. Comput..

[33]  Yangmin Li,et al.  Guaranteed cost synchronization of complex networks with uncertainties and time-Varying delays , 2016, Complex..

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

[35]  Weisheng Chen,et al.  Exponential synchronization of complex dynamical networks with time-varying inner coupling via event-triggered communication , 2017, Neurocomputing.