JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE) ›› 2017, Vol. 47 ›› Issue (3): 1-8.doi: 10.6040/j.issn.1672-3961.0.2016.320

    Next Articles

Finite-time stochastic generalized outer synchronization of time-delayed complex dynamical networks

LI Wang1,2, MA Zhicai2, SHI Hongjun2   

  1. 1. Basic Department, Jiangsu Xuzhou Medical College, Xuzhou 221008, Jiangsu, China;
    2. School of Mathematics, China University of Mining and Technology, Xuzhou 221008, Jiangsu, China
  • Received:2016-08-04 Online:2017-06-20 Published:2016-08-04

PDF (PC)

588

Abstract: Based on the finite-time control technology and the open-loop control method, the generalized outer synchronization between two complex dynamical networks with time delay and noise perturbation was investigated. A new finite-time controller was designed and the sufficient condition for the finite-time stochastic generalized outer synchronization was obtained based on the finite-time stability theory of stochastic differential equations. The results showed that the synchronization scheme was robust to the noise perturbation. The theoretical results showed that the synchronization time depended on the control strength. Under the same conditions, the synchronization time decreased with the increasing of the control strength. In the numerical examples, the R(¨overo)ssler-like system and Hindmarsh-Rose system were chosen as the node dynamics of the drive and response networks, respectively. The time evolution trajectories of synchronization error and total synchronization error were given. The effectiveness and feasibility of the theoretical result was confirmed by the numerical results.

Key words: complex networks, noise, synchronization, time delay

CLC Number: 

  • TP13
[1] WATTS D J, STROGATZ S H. Collective dynamics of small-world networks[J]. Nature, 1998, 393(6684): 440-442.
[2] ARENAS A, DAZ-GUILERA A, KURTHS J, et al. Synchronization in complex networks[J]. Physics Reports, 2008, 469(3): 93-153.
[3] 孙美美, 胡云安, 韦建明. 多涡卷超混沌系统自适应滑模同步控制[J]. 山东大学学报(工学版), 2015, 45(6): 45-51. SUN Meimei, HU Yunan, WEI Jianming. Synchronization of multiwing hyperchaotic systems via adaptive sliding mode control[J]. Journal of Shandong University(Engineering Science), 2015, 45(6): 45-51.
[4] LI Changpin, SUN Weigang, KURTHS J. Synchronization between two coupled complex networks[J]. Physical Review E, 2007, 76(4):046204
[5] WU Xiaoqun, ZHENG Weixing, ZHOU Jin. Generalized outer synchronization between complex dynamical networks[J]. Chaos, 2009, 19(1): 013109.
[6] SUN Weigang, LI Shixing. Generalized outer synchronization between two uncertain dynamical networks[J]. Nonlinear Dynamics, 2014, 77(3): 481-489.
[7] WANG Guanjun,CAO Jinde,LU Jianquan. Outer synchronization between two identifical networks with circumstance noice[J]. Physica A, 2010, 389(7): 1480-1488.
[8] SUN Yongzheng, LI Wang, RUAN Jiong. Generalized outer synchronization between complex dynamic networks with time delay and noise perturbation[J]. Communications in Nonlinear Science & Numerical Simulation, 2013, 18(4): 989-998.
[9] 马奎森, 王林山. S-分布时滞随机BAM神经网络的指数同步[J]. 山东大学学报(理学版), 2014, 49(3): 73-78. MA Kuisen, WANG Linshan. Exponential synchronization of stochastic BAM neural networks with S-type distributed delays[J]. Journal of Shandong University(Natural Science), 2014, 49(3): 73-78.
[10] 赵永清,江明辉. 混合变时滞二重边复杂网络自适应同步反馈控制[J]. 山东大学学报(工学版),2010, 40(3): 61-68. ZHAO Yongqing, JIANG Minghui. Adaptive synchronous feedback control of mixed time-varying delayed and double-linked complex networks[J]. Journal of Shandong University(Engineering Science), 2010, 40(3):61-68.
[11] 周璇, 谭满春, 田文秀. 双重时滞和非时滞耦合的复杂网络同步研究[J]. 计算机工程与应用, 2015, 51(10):30-35. ZHOU Xuan, TAN Manchun, TIAN Wenxiu. Research on synchronization of complex network with double delayed and double non-delayed coupling[J]. Computer Engineering and Applications, 2015, 51(10):30-35.
[12] HAUSCHILDT B, JASON N B, BALANOV A, et al. Noise-induced cooperative dynamics and its control in coupled neuron models[J]. Physical Review E, 2006, 74(5): 051906.
[13] KORNISS G. Synchronization in weighted uncorrelated complex networks in a noisy environment: optimization and connections with transport efficiency[J]. Physical Review E, 2007, 75(75): 051121.
[14] LIN Wei, CHEN Guanrong. Using white noise to enhance synchronization of coupled chaotic systems[J]. Chaos, 2006, 16(1): 013134.
[15] SUN Yongzheng, SHI Hongjun, BAKARE E A, et al. Noise-induced outer synchronization between two different complex dynamical networks[J]. Nonlinear Dynamics, 2014, 76(1): 519-528.
[16] 李望,石咏,马继伟. 复杂动力学网络的有限时间外部同步[J].山东大学学报(工学版),2013,43(2):48-53. LI Wang, SHI Yong, MA Jiwei. Finite-time outer synchronization of complex dynamical networks[J]. Journal of Shandong University(Engineering Science), 2013, 43(2):48-53.
[17] SANJAY P B, DENNIS S B. Finite-time stability of continuous autonomous systems[J]. SIAM Journal on Applied Mathematics, 2000, 38(3):751-766.
[18] HUANG Junjian, LI Chuandong, HUANG Tingwen, et al. Finite-time lag synchronization of delayed neural networks[J]. Neurocomputing, 2014, 139(13):145-149.
[19] WANG Hua, HAN Zhengzhi, XIE Qiyue, et al. Finite-time chaos control via nonsingular terminal sliding mode control[J]. Communications in Nonlinear Science & Numerical Simulation, 2009, 14(6):2728-2733.
[20] YANG Xinsong, CAO Jinde. Finite-time stochastic synchronization of complex networks[J]. Applied Mathematical Modelling, 2010, 34(11): 3631-3641.
[21] HARDY G, LITTLEWOOD J, POLYA G. Inequalities[M]. Cambridge:Cambridge University Press, 1952.
[22] ØKSENDAL B. Stochastic differential equations[M]. New York: Springer-Verlag Heidelberg, 2000.
[1] WANG Dongxiao. Two methods for sliding mode synchronization of five-dimensional fractional-order chaotic systems with entanglement iterms [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(5): 85-90.
[2] WANG Chunyan, DI Jinhong. Synchronization control of fractional-order multi-scroll chaotic system based on reduced-order method [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(5): 91-94.
[3] MENG Xiaoling, WANG Jianjun. Chaos synchronization of a class of fractional-order coronary artery systems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(4): 55-60.
[4] MAO Beixing. Ratio integral sliding mode synchronization control of entanglement chaotic systems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(4): 50-54.
[5] FENG Xia, HUANG Xixiang. Airport noise isoline parallel generating algorithm based on grid edge labeling [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2018, 48(2): 8-13.
[6] LI Wei, WANG Kehong, CAO Huichao. A fault filtering method based on an improved extended state filter for nonlinear system [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(5): 7-14.
[7] ZHAO Yinghong, HE Xiao, ZHOU Donghua. Fault tolerant estimation for a class of networked systems with sensor faults [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(5): 71-78.
[8] QIN Liguo, HE Xiao, ZHOU Donghua. A new distributed formation for multi-agent systems with constant time delays [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(5): 79-88.
[9] HUANG Chengkai, YANG Hao, JIANG Bin, CHENG Shuyao. Fault tolerant cooperative control for a class of complex networks [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(5): 203-209.
[10] ZHAO Ye, HE Xiao, ZHOU Donghua. On least squares fault estimation with incorrect measurement noise statistics [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(5): 254-262.
[11] MAO Beixing, CHENG Chunrui. Self-adaptive sliding mode control of fractional-order Victor-Carmen chaotic systems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(4): 31-36.
[12] LI Zhenwei, CUI Guozhong, GUO Congzhou, YU Changhao. Blind image restoration using alternating direction method of multipliers [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(4): 14-18.
[13] ZHANG Yuting, LI Wang, WANG Chenguang, LIU Youquan, SHI Hongjun. Synchronization of time-delayed complex dynamical networks with discontinuous coupling [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(4): 43-49.
[14] HAO Chongqing, WANG Zhihong. Classification and analysis of epileptic EEG based on complex networks [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(3): 8-15.
[15] LI Qingbin, WANG Xiaodong. Terminal sliding model control chaos synchronization of fractional-order emotion mode systems [J]. JOURNAL OF SHANDONG UNIVERSITY (ENGINEERING SCIENCE), 2017, 47(3): 84-88.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of Journal of Shandong University (Engineering Science)
Supported by Beijing Magtech Co.Ltd