Search

Article

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

Generalized projective lag synchronization between delay-coupled networks under circumstance noise

Zhang Li Yang Xiao-Li Sun Zhong-Kui

Generalized projective lag synchronization between delay-coupled networks under circumstance noise

Zhang Li, Yang Xiao-Li, Sun Zhong-Kui
PDF
Get Citation
  • It is well known that time delay and random noise are universal in complex networks. However, the research on the synchronization of coupled networks that are subjected to delay-coupling and noise perturbation is very rare. In this paper, for two delay-coupled complex networks with different node dynamics, different topological structures and different numbers of nodes, under circumstance noise, the generalized projective lag synchronization between two networks is proposed for the first time. First, a more realistic theoretical framework is constructed for the drive-response network synchronization. Second, according to the LaSalle-type theorem for stochastic differential delay equations, we rigorously prove that the generalized projective lag synchronization between the drive-response networks can be achieved almost surely, by introducing an appropriate controller. Furthermore, numerical simulation is employed to verify the theoretical analysis. The results indicate that the drive-response networks can indeed achieve generalized projective lag synchronization, and that the synchronization is independent of time delay and scaling factor. Moreover, the remarkable influences of the update gain and the coupling delay on synchronization speed are revealed through the numerical results.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11272258, 11172342) and the Fundamental Research Fund for the Central Universities, China (Grant No. GK201302001).
    [1]

    Huygens C 1669 Instructions Concerning the Use of Pendulum-Watches for Finding the Longitude at Sea 4 (London: Philos. Trans. R. Soc.) p937

    [2]

    Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1

    [3]

    Watts D J, Strogatz S H 1998 Nature 393 440

    [4]

    Barabási A L, Albert R 1999 Science 286 509

    [5]

    Luo Q, Wu W, Li L X, Yang Y X, Peng H P 2008 Acta Phys. Sin. 57 1529 (in Chinese) [罗群, 吴薇, 李丽香, 杨义先, 彭海朋 2008 物理学报 57 1529]

    [6]

    Jing X D, L L 2009 Acta Phys. Sin. 58 7539 (in Chinese) [敬晓丹, 吕翎 2009 物理学报 58 7539]

    [7]

    Li Y, L L, Luan L 2009 Acta Phys. Sin. 58 4463 (in Chinese) [李岩, 吕翎, 栾玲 2009 物理学报 58 4463]

    [8]

    L L, Zhang C 2009 Acta Phys. Sin. 58 1462 (in Chinese) [吕翎, 张超 2009 物理学报 58 1462]

    [9]

    Liu J G 2012 Chin. Phys. B 21 129506

    [10]

    Arenas A, Guilera A, Kurths J, Moreno Y, Zhou C S 2008 Phys. Rep. 469 93

    [11]

    Chen G R, Wang X F, Li X, L J H 2009 Some Recent Advances in Complex Networks Synchronization (Berlin Heidelberg: Springer-Verlag) pp3–16

    [12]

    Li C P, Sun W G, Kurths J 2007 Phys. Rev. E 76 046204

    [13]

    Wu X J, Lu H T 2010 Chin. Phys. B 19 070511

    [14]

    Tang H W, Chen L, Lu J A, Tse C K 2008 Physica A 387 5623

    [15]

    Li Y, Liu Z R, Zhang J B 2008 Chin. Phys. Lett. 25 874

    [16]

    Sun M, Zeng C Y, Tian L X 2010 Commun. Nonlinear Sci. Numer. Simul. 15 2162

    [17]

    Wu X Q, Zheng W X, Zhou J 2009 Chaos 19 013109

    [18]

    Wu Y Q, Li C P, Wu Y J, Kurths J 2012 Commun. Nonlinear Sci. Numer. Simul. 17 349

    [19]

    Zheng S, Bi Q S, Cai G L 2009 Phys. Lett. A 373 1553

    [20]

    Sun M, Zeng C Y, Tian L X 2009 Chin. Phys. Lett. 26 010501

    [21]

    Wu X J, Lu H T 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3005

    [22]

    Dai H, Jia L X, Zhang Y B 2012 Chin. Phys. B 21 120508

    [23]

    Yang Z Q, Zhang Q, Chen Z Q 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2628

    [24]

    Chen J R, Jiao L C, Wu J S, Wang X H 2009 Chin. Phys. Lett. 26 060505

    [25]

    Wu X J, Lu H T 2010 Phys. Lett. A 374 3932

    [26]

    Maritan A, Banavar J R 1994 Phys. Rev. Lett. 72 1451

    [27]

    Zhou C S, Kurths J 2002 Phys. Rev. Lett. 88 230602

    [28]

    Yang X L, Xu W, Sun Z K 2006 Phys. Lett. A 353 179

    [29]

    Guan S G, Lai Y C, Lai C H 2006 Phys. Rev. E 73 046210

    [30]

    Yang X L, Xu W 2008 Chin. Phys. B 17 2004

    [31]

    Lin W, Chen G R 2006 Chaos 16 013134

    [32]

    Xiao Y Z, Tang S F, Xu Y Chaos 22 013110

    [33]

    Sun Z K, Yang X L 2011 Chaos 21 033114

    [34]

    Wang G J, Cao J D, Lu J Q 2010 Physica A 389 1480

    [35]

    Cao L, Ma Y 2012 Int. J. Nonlinear Sci. 13 373

    [36]

    Sun Y Z, Li W, Ruan J 2013 Commun. Nonlinear Sci. Numer. Simul. 18 989

    [37]

    Arnold L 1972 Stochastic Differential Equation and Applications (New York: Wiley)

    [38]

    Friedman A 1975 Stochastic Differential Equations and Applications (New York: Academic Press)

    [39]

    Shen Y, Luo Q, Mao X R 2006 J. Math. Appl. 318 134

    [40]

    Mao X R 2002 J. Math. Appl. 268 125

  • [1]

    Huygens C 1669 Instructions Concerning the Use of Pendulum-Watches for Finding the Longitude at Sea 4 (London: Philos. Trans. R. Soc.) p937

    [2]

    Boccaletti S, Kurths J, Osipov G, Valladares D L, Zhou C S 2002 Phys. Rep. 366 1

    [3]

    Watts D J, Strogatz S H 1998 Nature 393 440

    [4]

    Barabási A L, Albert R 1999 Science 286 509

    [5]

    Luo Q, Wu W, Li L X, Yang Y X, Peng H P 2008 Acta Phys. Sin. 57 1529 (in Chinese) [罗群, 吴薇, 李丽香, 杨义先, 彭海朋 2008 物理学报 57 1529]

    [6]

    Jing X D, L L 2009 Acta Phys. Sin. 58 7539 (in Chinese) [敬晓丹, 吕翎 2009 物理学报 58 7539]

    [7]

    Li Y, L L, Luan L 2009 Acta Phys. Sin. 58 4463 (in Chinese) [李岩, 吕翎, 栾玲 2009 物理学报 58 4463]

    [8]

    L L, Zhang C 2009 Acta Phys. Sin. 58 1462 (in Chinese) [吕翎, 张超 2009 物理学报 58 1462]

    [9]

    Liu J G 2012 Chin. Phys. B 21 129506

    [10]

    Arenas A, Guilera A, Kurths J, Moreno Y, Zhou C S 2008 Phys. Rep. 469 93

    [11]

    Chen G R, Wang X F, Li X, L J H 2009 Some Recent Advances in Complex Networks Synchronization (Berlin Heidelberg: Springer-Verlag) pp3–16

    [12]

    Li C P, Sun W G, Kurths J 2007 Phys. Rev. E 76 046204

    [13]

    Wu X J, Lu H T 2010 Chin. Phys. B 19 070511

    [14]

    Tang H W, Chen L, Lu J A, Tse C K 2008 Physica A 387 5623

    [15]

    Li Y, Liu Z R, Zhang J B 2008 Chin. Phys. Lett. 25 874

    [16]

    Sun M, Zeng C Y, Tian L X 2010 Commun. Nonlinear Sci. Numer. Simul. 15 2162

    [17]

    Wu X Q, Zheng W X, Zhou J 2009 Chaos 19 013109

    [18]

    Wu Y Q, Li C P, Wu Y J, Kurths J 2012 Commun. Nonlinear Sci. Numer. Simul. 17 349

    [19]

    Zheng S, Bi Q S, Cai G L 2009 Phys. Lett. A 373 1553

    [20]

    Sun M, Zeng C Y, Tian L X 2009 Chin. Phys. Lett. 26 010501

    [21]

    Wu X J, Lu H T 2012 Commun. Nonlinear Sci. Numer. Simul. 17 3005

    [22]

    Dai H, Jia L X, Zhang Y B 2012 Chin. Phys. B 21 120508

    [23]

    Yang Z Q, Zhang Q, Chen Z Q 2012 Commun. Nonlinear Sci. Numer. Simul. 17 2628

    [24]

    Chen J R, Jiao L C, Wu J S, Wang X H 2009 Chin. Phys. Lett. 26 060505

    [25]

    Wu X J, Lu H T 2010 Phys. Lett. A 374 3932

    [26]

    Maritan A, Banavar J R 1994 Phys. Rev. Lett. 72 1451

    [27]

    Zhou C S, Kurths J 2002 Phys. Rev. Lett. 88 230602

    [28]

    Yang X L, Xu W, Sun Z K 2006 Phys. Lett. A 353 179

    [29]

    Guan S G, Lai Y C, Lai C H 2006 Phys. Rev. E 73 046210

    [30]

    Yang X L, Xu W 2008 Chin. Phys. B 17 2004

    [31]

    Lin W, Chen G R 2006 Chaos 16 013134

    [32]

    Xiao Y Z, Tang S F, Xu Y Chaos 22 013110

    [33]

    Sun Z K, Yang X L 2011 Chaos 21 033114

    [34]

    Wang G J, Cao J D, Lu J Q 2010 Physica A 389 1480

    [35]

    Cao L, Ma Y 2012 Int. J. Nonlinear Sci. 13 373

    [36]

    Sun Y Z, Li W, Ruan J 2013 Commun. Nonlinear Sci. Numer. Simul. 18 989

    [37]

    Arnold L 1972 Stochastic Differential Equation and Applications (New York: Wiley)

    [38]

    Friedman A 1975 Stochastic Differential Equations and Applications (New York: Academic Press)

    [39]

    Shen Y, Luo Q, Mao X R 2006 J. Math. Appl. 318 134

    [40]

    Mao X R 2002 J. Math. Appl. 268 125

  • [1] Zhang Meng, Yao Ruo-He, Liu Yu-Rong. A channel thermal noise model of nanoscaled metal-oxide-semiconductor field-effect transistor. Acta Physica Sinica, 2020, 69(5): 057101. doi: 10.7498/aps.69.20191512
    [2] Calibration source for OH radical based on synchronous photolysis. Acta Physica Sinica, 2020, (): . doi: 10.7498/aps.69.20200153
    [3] Zhang Zhan-Gang, Lei Zhi-Feng, Tong Teng, Li Xiao-Hui, Wang Song-Lin, Liang Tian-Jiao, Xi Kai, Peng Chao, He Yu-Juan, Huang Yun, En Yun-Fei. Comparison of neutron induced single event upsets in 14 nm FinFET and 65 nm planar static random access memory devices. Acta Physica Sinica, 2020, 69(5): 056101. doi: 10.7498/aps.69.20191209
    [4] Yang Yong-Xia, Li Yu-Ye, Gu Hua-Guang. Synchronization transition from bursting to spiking and bifurcation mechanism of the pre-Bötzinger complex. Acta Physica Sinica, 2020, 69(4): 040501. doi: 10.7498/aps.69.20191509
  • Citation:
Metrics
  • Abstract views:  532
  • PDF Downloads:  418
  • Cited By: 0
Publishing process
  • Received Date:  11 July 2013
  • Accepted Date:  19 September 2013
  • Published Online:  20 December 2013

Generalized projective lag synchronization between delay-coupled networks under circumstance noise

  • 1. College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China;
  • 2. Department of Applied Mathematics, Northwestern Polytechnical University, Xi’an 710072, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11272258, 11172342) and the Fundamental Research Fund for the Central Universities, China (Grant No. GK201302001).

Abstract: It is well known that time delay and random noise are universal in complex networks. However, the research on the synchronization of coupled networks that are subjected to delay-coupling and noise perturbation is very rare. In this paper, for two delay-coupled complex networks with different node dynamics, different topological structures and different numbers of nodes, under circumstance noise, the generalized projective lag synchronization between two networks is proposed for the first time. First, a more realistic theoretical framework is constructed for the drive-response network synchronization. Second, according to the LaSalle-type theorem for stochastic differential delay equations, we rigorously prove that the generalized projective lag synchronization between the drive-response networks can be achieved almost surely, by introducing an appropriate controller. Furthermore, numerical simulation is employed to verify the theoretical analysis. The results indicate that the drive-response networks can indeed achieve generalized projective lag synchronization, and that the synchronization is independent of time delay and scaling factor. Moreover, the remarkable influences of the update gain and the coupling delay on synchronization speed are revealed through the numerical results.

Reference (40)

Catalog

    /

    返回文章
    返回