不连续耦合的时滞复杂动态网络的同步

doi:10.6040/j.issn.1672-3961.0.2016.122

山东大学学报(工学版) ›› 2017, Vol. 47 ›› Issue (4): 43-49.doi: 10.6040/j.issn.1672-3961.0.2016.122

不连续耦合的时滞复杂动态网络的同步

张玉婷^1,3,李望^1,2,王晨光¹,刘友权¹,侍红军^1*

1. 中国矿业大学数学学院, 江苏徐州 221116;2. 江苏徐州医药高等学校基础部, 江苏徐州 221116;3. 哈尔滨工业大学人文社科与法学学院, 黑龙江哈尔滨 150001

收稿日期:2016-04-13 出版日期:2017-08-20 发布日期:2016-04-13
通讯作者: 侍红军(1979— ),男,江苏淮安人,讲师,博士研究生,主要研究方向为复杂网络同步与控制,图论染色.E-mail:hjshi79@gmail.com E-mail:zhangyutingzjl@163.com
作者简介:张玉婷(1995— ),女,山东邹城人,硕士研究生,主要研究方向为复杂网络同步. E-mail:zhangyutingzjl@163.com
基金资助:
中央高校基本科研业务费资助项目(2015xkms076);国家级大学生创新创业训练计划资助项目(201710290089)

Synchronization of time-delayed complex dynamical networks with discontinuous coupling

ZHANG Yuting^1,3, LI Wang^1,2, WANG Chenguang¹, LIU Youquan¹, SHI Hongjun^1*

1. School of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China;
2. Basic Department, Jiangsu Xuzhou Medical College, Xuzhou 221116, Jiangsu, China;
3. School of Humanities and Social Science and Law, Harbin Institute of Technology, Harbin 150001, Heilongjiang, China

Received:2016-04-13 Online:2017-08-20 Published:2016-04-13

摘要/Abstract

摘要： 基于李雅普诺夫稳定性理论,对不连续耦合的时滞复杂动态网络进行分析,得到网络同步的充分条件,并且给出网络实现同步时滞的上界估计。研究表明:即使网络之间的耦合是不连续的,只要时滞满足一定条件,网络也可以实现同步,且网络容许的时滞上界与耦合强度、网络代数连通性以及耦合的开关率相关。数值模拟中利用Ikeda系统作为节点动力学,采用误差函数作为网络同步性指标,给出网络同步误差演化轨迹和各状态的演化轨迹,并进一步分析控制参数对同步速度的影响,模拟结果验证了理论结果的正确性。

关键词: 同步, 李雅普诺夫稳定性, 复杂网络, 时滞, 不连续耦合

Abstract: The synchronization problem of complex dynamical networks with time delay and discontinuous coupling was investigated based on Lyapunov stability theory. The sufficient conditions for the networks synchronization was established and the upper bound estimation of the time delay was obtained. The acquired analytical results showed that network with discontinuous coupling could achieve synchronization if time delay met some conditions. The upper bound of the delay for synchronization depended on the coupling strength, the algebraic connectivity of network and on-off rate. The application of numerical simulation results proved that evolution trajectory of network synchronization error and different conditions, in which Ikeda system was used as node dynamics and error function as the network synchronization index. Furthermore, the effect of control parameters on the synchronization speed was analyzed. Numerical examples were provided to verify the effectiveness of the theoretical results.

Key words: discontinuous coupling, synchronization, Lyapunov stability theory, complex networks, time delay

中图分类号:

TP273

张玉婷,李望,王晨光,刘友权,侍红军. 不连续耦合的时滞复杂动态网络的同步[J]. 山东大学学报(工学版), 2017, 47(4): 43-49.

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.

参考文献

[1] WATTS D J, STROGATZ S H. Collective dynamics of small-world networks[J]. Nature, 1998, 393(6684):440-442.
[2] BARABÁSIA L, ALBERT R. Emergence of scaling in random networks[J]. Science, 1999, 286(5439): 509-512.
[3] 郭雷, 许晓鸣. 复杂网络[M]. 上海:上海科技教育出版社, 2006.
[4] 汪小帆, 李翔, 陈关荣. 复杂网络理论及其应用[M]. 北京:清华大学出版社, 2006.
[5] ARENAS A, DÍAZ-GUILERA A, KURTHS J, et al. Synchronization in complex networks[J]. Physics Reports, 2008, 469(3): 93-153.
[6] 何大韧, 刘宗华, 汪秉宏. 复杂系统与复杂网络[M]. 北京: 高等教育出版社, 2009.
[7] 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 Shangdong University(Engineering Science), 2010, 40(3):61-68.
[8] 李望, 石咏, 马继伟. 复杂动态网络的有限时间外部同步[J]. 山东大学学报(工学版), 2013, 43(2):61-68. LI Wang, SHI Yong, MA Jiwei. Finite-time outer synchronization of complex dynamical networks[J]. Journal of Shangdong University(Engineering Science), 2013, 43(2):61-68.
[9] 孙炜伟, 王玉振. 几类时滞非线性哈密顿系统的稳定性分析[J]. 山东大学学报(理学版), 2007, 42(12):1-9. SUN Weiwei, WANG Yuzhen. Stability analysis for some classes of time-delay nonlinear Hamiltonian systems[J]. Journal of Shangdong University(Natural Science), 2007, 42(12):1-9.
[10] PECORA L M, CARROLL T L. Master stability functions for synchronized coupled systems[J]. Physical Review Letters, 1998, 80(10): 2109-2112.
[11] WANG Xiaofan, CHEN Guanrong. Synchronization in small-world dynamical networks[J]. International Journal of Bifurcation & Chaos, 2002, 12(1):187-192.
[12] WANG Xiaofan, CHEN Guanrong. Synchronization in scale-free dynamical networks: robustness and fragility[J]. IEEE Transactions on Circuits System I, 2002, 49(1):54-62.
[13] LU Jinhu, CHEN Guanrong. A time-varying complex dynamical network model and its controlled synchronization criteria[J]. IEEE Transactions on Automatic Control, 2005, 50(6):841-846.
[14] WU Xiaoqun, ZHENG Weixing, ZHOU Jin. Generalized outer synchronization between complex dynamical networks[J]. Chaos an Interdisciplinary Journal of Nonlinear Science, 2009, 19(1):193-204.
[15] 涂俐兰, 陆君安. 一类时滞动力网络的时滞相关稳定性[J]. 复杂系统与复杂性科学, 2007, 4(2):33-38. TU Lilan, LU Junan. Delay-dependent stability conditrons in general concplex delayed dynamical networks[J]. Complex System and Complexity Science, 2007, 4(2):33-38.
[16] ZHANG Lixian, BOUKAS E K, LAM J. Analysis and synthesis of Markov jump linear systems with time-varying delays and partially known transition probabilities[J]. IEEE Transactions on Automatic Control, 2008, 53(10):2458-2464.
[17] CHIOU J S. Stability analysis for a class of switched large-scale time-delay systems via time-switched method[J]. IEEE Proceedings: Control Theory and Applications, 2006, 153(6):684-688.
[18] CAO Jinde, WANG Zidong, SUN Yonghui. Synchronization in an array of of linearly stochastically coupled networks with time delay[J]. Physica A, 2007, 385(2): 718-728.
[19] YU Wenwu, CAO Jinde. Synchronization control of stochastic delayed neural networks[J]. Physica A, 2007, 373(1):252-260.
[20] HUNT D, KOMISS G, SZYMANSKI B K. Network synchronization in a noisy environment with time delays: fundamental limits and trade-offs[J]. Physical Review Letters, 2010, 105(6):2155-2212.
[21] CHEN Liquan, QIU Chengfeng, HUANG H B. Synchronization with on-off coupling: role of time scales in network dynamics[J]. Physical Review E: Statistical Nonlinear & Soft Matter Physics, 2009, 79(4 Pt 2):045-101.
[22] CHEN Liquan, QIU Chengfeng, HUANG H B. Facilitated synchronization of complex networks through a discontinuous coupling strategy[J]. The European Physical Journal B, 2010, 76(4):625-635.
[23] SUN Yongzheng, WANG Li, ZHAO Donghua. Outer synchronization between two complex dynamical networks with discontinuous coupling[J]. Chaos an Interdisciplinary Journal of Nonlinear Science, 2012, 22(4):517-525.
[24] 张颖, 段广仁. 时滞离散切换系统基于观测器的输出反馈镇定[J]. 山东大学学报(工学版), 2005, 35(3):40-43. ZHANG Ying, DUAN Guangren. Observer-based output feedback stabilization for a class of discrete-time switched systems with time-delay[J]. Journal of Shangdong University(Engineering Science), 2005, 35(3):40-43.
[25] ZHOU Jin, CHEN Tianping. Synchronization in general complex delayed dynamical networks[J]. Circuits & Systems I Regular Papers IEEE Transactions on, 2006, 53(3):733-744.
[26] CHIOU J, WANG C, CHENG Chunming. On delay-dependent stabilization analysis for the switched time-delay systems with the state-driven switching strategy[J]. Journal of the Franklin Institute, 2011, 348(9):2292-2307.

多维度评价

Viewed

Full text

Abstract

Cited

Shared

Discussed

不连续耦合的时滞复杂动态网络的同步

Synchronization of time-delayed complex dynamical networks with discontinuous coupling

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

多维度评价

本文评价

推荐阅读 0

[1]	王东晓. 具有纠缠项的分数阶五维混沌系统滑模同步的两种方法[J]. 山东大学学报(工学版), 2018, 48(5): 85-90.
[2]	王春彦,邸金红. 基于降阶方法的分数阶多涡卷混沌系统的同步控制[J]. 山东大学学报(工学版), 2018, 48(5): 91-94.
[3]	孟晓玲,王建军. 一类分数阶冠状动脉系统的混沌同步控制[J]. 山东大学学报(工学版), 2018, 48(4): 55-60.
[4]	毛北行. 纠缠混沌系统的比例积分滑模同步[J]. 山东大学学报(工学版), 2018, 48(4): 50-54.
[5]	宋正强,杨辉玲,肖丹. 基于在线粒子群优化方法的IPMSM驱动电流和速度控制器[J]. 山东大学学报(工学版), 2018, 48(1): 112-116.
[6]	毛海杰,李炜,王可宏,冯小林. 基于自抗扰的多电机转速同步系统传感器故障切换容错策略[J]. 山东大学学报(工学版), 2017, 47(5): 64-70.
[7]	黄成凯,杨浩,姜斌,程舒瑶. 一类复杂网络的协同容错控制[J]. 山东大学学报(工学版), 2017, 47(5): 203-209.
[8]	毛北行,程春蕊. 分数阶Victor-Carmen混沌系统的自适应滑模控制[J]. 山东大学学报(工学版), 2017, 47(4): 31-36.
[9]	侯广松,高军,吴衍达,张欣,邓影,李常刚,张亚萍. 输电线路参数与运行方式的相关性分析[J]. 山东大学学报(工学版), 2017, 47(4): 89-95.
[10]	李望,马志才,侍红军. 时滞复杂动态网络的有限时间随机广义外部同步[J]. 山东大学学报(工学版), 2017, 47(3): 1-8.
[11]	郝崇清,王志宏. 基于复杂网络的癫痫脑电分类与分析[J]. 山东大学学报(工学版), 2017, 47(3): 8-15.
[12]	李庆宾,王晓东. 分数阶情绪模型的终端滑模控制混沌同步[J]. 山东大学学报(工学版), 2017, 47(3): 84-88.
[13]	毛北行,王东晓. 分数阶多涡卷系统滑模控制混沌同步[J]. 山东大学学报(工学版), 2017, 47(3): 79-83.
[14]	张万志,刘华,张峰,高磊,姚晨,刘冠之. 斜拉桥塔梁同步施工过程的力学特性[J]. 山东大学学报(工学版), 2016, 46(6): 120-126.
[15]	侯明冬,王印松,田杰. 积分时滞对象的一种内模PID鲁棒控制方法[J]. 山东大学学报(工学版), 2016, 46(5): 64-67.