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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.
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Keywords:
- successive lag synchronization /
- linear feedback control /
- adaptive control /
- non-uniform communication delay
[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]
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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]
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[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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