非一致通信时滞动力学网络上的接连滞后同步

张迪; 张银星; 邱小芬; 祝光湖; 李科赞

doi:10.7498/aps.67.20171630

摘要

在动力学网络中，节点与节点之间的通信通常存在时滞，并且不同节点之间的通信时滞往往是不同的（即非一致通信时滞），研究非一致通信时滞动力学网络上的接连滞后同步，更具现实意义.为此，本文首先构建含有非一致通信时滞的动力学网络模型.其次分别设计线性反馈控制和自适应反馈控制，利用Lyapunov函数方法，重点分析了该网络的接连滞后同步的稳定性，得到了同步稳定的充分条件.最后，选取蔡氏电路作为局部动力学，又分别选取了链式网络和星型网络这两种拓扑结构来验证理论结果的正确性和有效性.

关键词:

Abstract

In dynamical networks, usually there are time delays among nodes during their communication. Different pairs of nodes generally have different time delays (i.e., having non-uniform communication delays). It has more practical significance to study the successive lag synchronization on dynamical networks with non-uniform communication delays. So, in this paper we construct a dynamical network model with non-uniform communication delay. Then, by designing linear feedback control and adaptive feedback control, and by using the Lyapunov function method, we obtain sufficient conditions for guaranteeing the stability of successive lag synchronization. Finally, in the numerical simulation, we choose the Chua's circuit as the local nonlinear dynamic and two kinds of topological structures for dynamical network to verify the effectiveness and correctness of obtained results.

Keywords:

作者及机构信息

1.
桂林电子科技大学数学与计算科学学院, 广西密码学与信息安全重点实验室, 桂林 541004

通信作者: 李科赞, kezanli@163.com

基金项目: 国家自然科学基金（批准号：61663006，11661026，11562006）、广西自然科学基金（批准号：2015GXNSFBB139002）和广西密码学与信息安全重点实验室（编号：GCIS201612）资助的课题.

Authors and contacts

1.
School of Mathematics and Computing Science, Guangxi Key Laboratory of Cryptography and Information Security, Guilin University of Electronic Technology, Guilin 541004, China

Corresponding author: Li Ke-Zan, kezanli@163.com

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 61663006, 11661026, 11562006), the Guangxi Natural Science Foundation Program, China (Grant No. 2015GXNSFBB139002), and Guangxi Key Laboratory of Cryptography and Information Security, China (Grant No. GCIS201612).

参考文献

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[11]	Li X W, Zheng Z G 2007 Commun. Theor. Phys. 47 265
[12]	Shahverdiev E M, Sivaprakasam S, Shore K A 2002 Phys. Lett.. 292 320
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[14]	Dai H, Jia L X, Zhang Y B 2012 Chin. Phys.. 21 120508
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[16]	Wu W, Chen T P 2009 Physica . 238 355
[17]	Yang X S, Zhu Q X 2011 Nonlinear Anal. RWA 12 93
[18]	Wu X J, Lu H T 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 3005
[19]	Pal S, Sahoo B, Poria S 2013 Phys. Scr. 87 45011
[20]	Li K Z, Yu W W, Ding Y 2015 Nonlinear Dyn. 80 421
[21]	Zhang X J, Wei A J, Li K Z 2016 Chin. Phys.. 25 038901
[22]	Yu W W, Chen G R, Cao M, Kurths J 2010 IEEE Trans. Syst. Man Cybern. B: Cybern. 40 881
[23]	Mei J, Ren W, Chen J, Ma G F 2013 Automatica 49 1723
[24]	Xie Y Y, Wang Y, Ma Z J 2014 Acta Phys. Sin. 63 040202(in Chinese) [谢媛艳, 王毅, 马忠军 2014 物理学报 63 040202]
[25]	Chen T P, Liu X W, Lu W L 2007 IEEE Trans. Circuits Syst.. 54 1317
[26]	Li K Z, Zhou J, Yu W W 2014 Appl. Math. Model. 38 1300
[27]	Tao G 1997 IEEE Trans. Automat. Control 42 698
[28]	Fang B R, Zhou J D, Li Y M 2013 Matrix Theory (Beijing: Tsinghua University Press) pp350-352 (in Chinese) [方保镕, 周继东, 李医民 2013 矩阵论 (北京: 清华大学出版社) 第350352页]

施引文献

[1]	Wang X F, Li X, Chen G R 2012 Network Science: An Introduction (Beijing: Higher Education Press) pp3-27 (in Chinese) [汪小帆, 李翔, 陈关荣 2012 网络科学导论 (北京: 高等教育出版社) 第327页]
[2]	Fang J Q, Wang X F, Zheng Z G, Bi Q, Di Z R, Li X 2007 Prog. Phys. 27 239(in Chinese) [方锦清, 汪小帆, 郑志刚, 毕桥, 狄增如, 李翔 2007 物理学进展 27 239]
[3]	Zhao M, Zhou T, Chen G R, Wang B H 2008 Prog. Phys. 28 22(in Chinese) [赵明, 周涛, 陈关荣, 汪秉宏 2008 物理学进展 28 22]
[4]	Liu J L 2012 Acta Phys. Sin. 61 040503(in Chinese) [刘金良 2012 物理学报 61 040503]
[5]	Feng J W, Yang P, Zhao Y 2016 Appl. Math. Comput. 291 52
[6]	Feng J W, Li N, Zhao Y, Xu C, Wang J Y 2017 Nonlinear Dyn. 88 2723
[7]	Wang J Y, Feng J W, Xu C, Chen M Z Q, Zhao Y, Feng J Q 2016 Automatica 66 155
[8]	Prcora L M, Carroll T L 1998 Phys. Rev. Lett. 80 2109
[9]	Xiao Y Z, Xu W, Li X C, Tang S F 2008 Chin. Phys.. 17 80
[10]	Chen J, Liu Z R 2005 J. Appl. Math. Mech. 26 1132
[11]	Li X W, Zheng Z G 2007 Commun. Theor. Phys. 47 265
[12]	Shahverdiev E M, Sivaprakasam S, Shore K A 2002 Phys. Lett.. 292 320
[13]	Li X, Chen Y 2007 Commun. Theor. Phys. 48 132
[14]	Dai H, Jia L X, Zhang Y B 2012 Chin. Phys.. 21 120508
[15]	Feng J W, Wu G, Zhang W Q, He L 2009 J. Shenzhen Univ. Sci. Engin. 26 36(in Chinese) [丰建文, 吴耿, 张维强, 何玲 2009 深圳大学学报理工版 26 36]
[16]	Wu W, Chen T P 2009 Physica . 238 355
[17]	Yang X S, Zhu Q X 2011 Nonlinear Anal. RWA 12 93
[18]	Wu X J, Lu H T 2012 Commun. Nonlinear Sci. Numer. Simulat. 17 3005
[19]	Pal S, Sahoo B, Poria S 2013 Phys. Scr. 87 45011
[20]	Li K Z, Yu W W, Ding Y 2015 Nonlinear Dyn. 80 421
[21]	Zhang X J, Wei A J, Li K Z 2016 Chin. Phys.. 25 038901
[22]	Yu W W, Chen G R, Cao M, Kurths J 2010 IEEE Trans. Syst. Man Cybern. B: Cybern. 40 881
[23]	Mei J, Ren W, Chen J, Ma G F 2013 Automatica 49 1723
[24]	Xie Y Y, Wang Y, Ma Z J 2014 Acta Phys. Sin. 63 040202(in Chinese) [谢媛艳, 王毅, 马忠军 2014 物理学报 63 040202]
[25]	Chen T P, Liu X W, Lu W L 2007 IEEE Trans. Circuits Syst.. 54 1317
[26]	Li K Z, Zhou J, Yu W W 2014 Appl. Math. Model. 38 1300
[27]	Tao G 1997 IEEE Trans. Automat. Control 42 698
[28]	Fang B R, Zhou J D, Li Y M 2013 Matrix Theory (Beijing: Tsinghua University Press) pp350-352 (in Chinese) [方保镕, 周继东, 李医民 2013 矩阵论 (北京: 清华大学出版社) 第350352页]

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