Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

doi:10.1088/1674-1056/23/2/020205

中国物理B ›› 2014, Vol. 23 ›› Issue (2): 20205-020205.doi: 10.1088/1674-1056/23/2/020205

Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

R. Rakkiyappan^a, N. Sakthivel^a, S. Lakshmanan^b

a Department of Mathematics, Bharathiar University, Coimbatore-641 046, Tamilnadu, India;
b Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, UAE

收稿日期:2013-06-12 修回日期:2013-07-09 出版日期:2013-12-12 发布日期:2013-12-12
基金资助:
Project supported by the NBHM Research Project (Grant Nos. 2/48(7)/2012/NBHM(R.P.)/R and D Ⅱ/12669).

Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

R. Rakkiyappan^a, N. Sakthivel^a, S. Lakshmanan^b

a Department of Mathematics, Bharathiar University, Coimbatore-641 046, Tamilnadu, India;
b Department of Mathematical Sciences, College of Science, UAE University, Al Ain 15551, UAE

Received:2013-06-12 Revised:2013-07-09 Online:2013-12-12 Published:2013-12-12
Contact: R. Rakkiyappan, S. Lakshmanan E-mail:rakkigru@gmail.com;lakshm85@gmail.com
About author:02.30.Ks; 05.45.Gg; 05.45.Xt
Supported by:
Project supported by the NBHM Research Project (Grant Nos. 2/48(7)/2012/NBHM(R.P.)/R and D Ⅱ/12669).

摘要/Abstract

摘要： In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sampling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

关键词: complex networks, exponential synchronization, mode-dependent time-varying delays, linear matrix inequalities, sampled-data control

Abstract: In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sampling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

Key words: complex networks, exponential synchronization, mode-dependent time-varying delays, linear matrix inequalities, sampled-data control

中图分类号: (Delay and functional equations)

02.30.Ks

05.45.Gg (Control of chaos, applications of chaos) 05.45.Xt (Synchronization; coupled oscillators)

R. Rakkiyappan, N. Sakthivel, S. Lakshmanan. Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays[J]. 中国物理B, 2014, 23(2): 20205-020205.

参考文献 48

[1]	Strogatz S H 2001 Nature 410 268
[2]	Boccaletti S, Latora V, Marenu Y, Chavez M and Huang D U 2006 Phys. Rep. 424 175
[3]	Newman M E J 2003 SIAM Rev. 45 167
[4]	Gao H, Lam J and Chen G 2006 Phys. Lett. A 360 263
[5]	Lu H and Ho D 2008 Chaos, Solitons and Fractals 37 1497
[6]	Wang B and Guan Z 2010 Nonlinear Analysis Real World Applications 11 1925
[7]	Yue D and Li H 2010 Neurocomputing 73 809
[8]	Lu J and Ho D W C 2010 IEEE Trans. Syst. Man Cybernet. Part B: Cybernet. 40 350
[9]	Xia F C, Hong W Y and Ping J G 2012 Chin. Phys. B 21 020510
[10]	Xiang Y H and Guo W S 2012 Chin. Phys. B 21 110506
[11]	Zhou W, Wang T, Mou J and Fang J 2012 J. Frank. Ins. 349 1267
[12]	Liang Y and Wang X Y 2013 Acta Phys. Sin. 62 018901 (in Chinese)
[13]	Liu Y, Wang Z and Liu X 2008 Phys. Lett. A 372 3986
[14]	Tang Y, Fang J and Miao Q Y 2009 Int. J. Neural Sys. 19 43
[15]	Liu Y, Wang Z and Liu X 2009 Int. J. Mod. Phys. B 23 411
[16]	Ma Q, Xu S and Zou Y 2011 Neurocomputing 74 3404
[17]	Lakshmanan S, Park J H, Jung H Y and Balasubramaniam P 2012 Chin. Phys. B 21 100205
[18]	Li Z X, Park J H and Wu Z G 2013 Nonlinear Dynamics 74 65
[19]	Yi J W, Wang Y W, Xiao J W and Huang Y 2013 Commun. Nonlinear Sci. Numer. Simul. 18 1175
[20]	Carroll T and Pecora L 1991 IEEE Trans. Circuit Sys. I: Fundamental Theory and Application, 38 453
[21]	Curran P, Suykens J and Chua L 1997 Int. J. Bifur. Chaos 7 2891
[22]	Xian L, Qing G and Liyong N 2010 Nonlinear Dynamics 59 297
[23]	Lu J and Hill D 2008 IEEE Trans. Circuit Sys. Ⅱ: Exp. Bri. 55 586
[24]	Zhang C, He Y and Wu M 2009 IEEE Trans. Circ. Sys. Ⅱ: Exp. Bri. 56 320
[25]	Jeeva Sathya Theesar S, Banerjee S and Balasubramaniam P 2012 Nonlinear Dynamics 70 1977
[26]	Fridman E, Seuret A and Richard J P 2004 Automatica 40 1441
[27]	Fridman E, Shaked U and Suplin V 2005 Sys. Control Lett. 54 271
[28]	Li N, Zhang Y, Hu J and Nie Z 2011 Neurocomputing 74 805
[29]	Shen B, Wang Z and Liu X 2012 IEEE Trans. Autom. Control 57 2644
[30]	Lee T H, Wu Z G and Park J H 2012 Appl. Math. Comput. 219 1354
[31]	Wu Z G, Park J H, Su H, Song B and Chu J 2012 J. Frank. Ins. 349 2735
[32]	Qing Z H and Wei J Y 2011 Chin. Phy. B 20 060504
[33]	Yang R, Zhang Z and Shi P 2010 IEEE Trans. Neuronal Network 21 169
[34]	Chen W H and Zheng W X 2010 IEEE Trans. Neuronal Network 21 508
[35]	Deng C B, Yang G and Ye Z Y 2011 Chin. Phy. B 20 010207
[36]	Tang M N 2012 Chin. Phys. B 20 020509
[37]	Yi S and Wang J 2012 IEEE Trans. Neuronal Network Leaning Sys. 23 87
[38]	Li C, Sun W and Kurths J 2006 Physica A 361 24
[39]	Li K, Guan S, Gong X and Lai C H 2008 Phys. Lett. A 372 7133
[40]	Yu W, Cao J and Lu J 2008 SIAM J. Appl. Dyn. Sys. 7 108
[41]	Li H and Yue D 2009 J. Comput. Appl. Math. 232 149
[42]	Jiao Z Q and Chan Z J 2012 Chin. Phys. B 21 040502
[43]	Guo W S and Xing Y H 2012 Chin. Phys. B 21 050508
[44]	Li H, Yue D and Gu Z 2009 Joint 48th IEEE Conference on Decision and Control and 28th Chinese Control Conference, Shanghai, China, December 16-18, 2009
[45]	Li H and Yue D 2010 J. Phys. A: Math. Theor. 43 105101
[46]	Li H 2011 J. Phys. A: Math. Theor. 44 105101
[47]	Li H J 2011 ICIC, International C 2011 ISSN 1349-4198 p. 697
[48]	Li H, Wang W K and Tang Y 2012 J. Opt. Theor. Appl. 152 496

Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献 48

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Jie Zhou(周洁), Cheng Yuan(袁诚), Zu-Yu Qian(钱祖燏), Bing-Hong Wang(汪秉宏), and Sen Nie(聂森). Analysis of cut vertex in the control of complex networks[J]. 中国物理B, 2023, 32(2): 28902-028902.
[2]	Pengli Lu(卢鹏丽) and Wei Chen(陈玮). Vertex centrality of complex networks based on joint nonnegative matrix factorization and graph embedding[J]. 中国物理B, 2023, 32(1): 18903-018903.
[3]	Ai-Xia Feng(冯爱霞), Qi-Guang Wang(王启光), Shi-Xuan Zhang(张世轩), Takeshi Enomoto(榎本刚), Zhi-Qiang Gong(龚志强), Ying-Ying Hu(胡莹莹), and Guo-Lin Feng(封国林). Characteristics of vapor based on complex networks in China[J]. 中国物理B, 2022, 31(4): 49201-049201.
[4]	Yahan Deng(邓雅瀚), Zhongkai Mo(莫中凯), and Hongqian Lu(陆宏谦). Robust H_∞ state estimation for a class of complex networks with dynamic event-triggered scheme against hybrid attacks[J]. 中国物理B, 2022, 31(2): 20503-020503.
[5]	Hongwei Zhang(张红伟), Ran Cheng(程然), and Dawei Ding(丁大为). Finite-time synchronization of uncertain fractional-order multi-weighted complex networks with external disturbances via adaptive quantized control[J]. 中国物理B, 2022, 31(10): 100504-100504.
[6]	Gui-Qiong Xu(徐桂琼), Lei Meng(孟蕾), Deng-Qin Tu(涂登琴), and Ping-Le Yang(杨平乐). LCH: A local clustering H-index centrality measure for identifying and ranking influential nodes in complex networks[J]. 中国物理B, 2021, 30(8): 88901-088901.
[7]	Tong-Feng Weng(翁同峰), Xin-Xin Cao(曹欣欣), and Hui-Jie Yang(杨会杰). Complex network perspective on modelling chaotic systems via machine learning[J]. 中国物理B, 2021, 30(6): 60506-060506.
[8]	杨远志, 胡敏, 黄泰愚. Influential nodes identification in complex networks based on global and local information[J]. 中国物理B, 2020, 29(8): 88903-088903.
[9]	闫小丽, 崔亚鹏, 倪顺江. Identifying influential spreaders in complex networks based on entropy weight method and gravity law[J]. 中国物理B, 2020, 29(4): 48902-048902.
[10]	石勇, 李博, 龙文. Pyramid scheme model for consumption rebate frauds[J]. 中国物理B, 2019, 28(7): 78901-078901.
[11]	朱世钊, 王玉青, 汪秉宏. Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms[J]. 中国物理B, 2019, 28(10): 108901-108901.
[12]	庞明宝, 黄玉满. Coordinated chaos control of urban expressway based on synchronization of complex networks[J]. 中国物理B, 2018, 27(11): 118902-118902.
[13]	王兴元, 王宇, 秦小蒙, 李睿, Justine Eustace. Detecting overlapping communities based on vital nodes in complex networks[J]. 中国物理B, 2018, 27(10): 100504-100504.
[14]	郑志刚, 钱郁. Dominant phase-advanced driving analysis of self-sustained oscillations in biological networks[J]. 中国物理B, 2018, 27(1): 18901-018901.
[15]	童评, 陈士华. New results for exponential synchronization of linearly coupled ordinary differential systems[J]. 中国物理B, 2017, 26(5): 50503-050503.