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

Frozen random patterns in a globally coupled discontinuous map lattices system

Tan Hong-Fang Jin Tao Qu Shi-Xian

Frozen random patterns in a globally coupled discontinuous map lattices system

Tan Hong-Fang, Jin Tao, Qu Shi-Xian
PDF
Get Citation
  • A class of the characteristic collective dynamic behaviors, i.e., the frozen random patterns, in a globally coupled both-discontinuous-and-non-invertible-map lattices are studied. The coupling-strength dependences of the mean order parameters and the largest Lyapunov exponents are calculated and analyzed. The result shows that, given the initial values for the dynamical variables, the system will reach its complete or partial synchronization state when the coupling strength is beyond some critical value, where the frozen random pattern appears. These phenomena reveal that there are coexisting attractors in the system, and thus the structure and the distribution of the frozen random patterns sensitively depend on the choice of the initial dynamics variables. The interesting event is that the system can be modulated to some regular states of motion by the coupling among lattices even when the single maps are in the chaotic states, which may have some important applications in controlling chaos. The rich dynamical behaviors mentioned above are due to the interplay between the discontinuity and the non-invertibility in the map.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No.10875076), and the Natural Science Foundation of Shaanxi Province (Grant No.SJ08A23).
    [1]

    Kanoke K 1992 Chaos 2 279

    [2]

    Kanoke K 1991 Physica D 54 5

    [3]

    Hu G, Qu Z L 1994 Phys. Rev. Lett. 72 68

    [4]

    Batista A M, Pinto S E de S, Viana R L, Lopes S R 2002 Phys. Rev. E 65 056209

    [5]

    Santos A M,Viana R L, Lopes S R, Pinto S E de S, Batista A M 2006 Physica A 367 145

    [6]

    Yang W M 1994 Spatio-temproal Chaos and Coupled Map Lattices (Shanghai: Education And Technology Press of Shanghai) (in Chinese) [杨维明 1994 时空混沌和耦合映像格子(上海: 上海教育科技出版社)]

    [7]

    Wiesenfeld K, Hadley P 1989 Phys. Rev. Lett. 62 1335

    [8]

    Sompolinsky H, Golomb D 1991 Phys. Rev. A 43 6990

    [9]

    Wiesenfeld K, Bracikowski C, James G, Roy R 1990 Phys. Rev. Lett. 65 1749

    [10]

    Sompolinsky H, Golomb D, Kleinfeld D 1991 Phys. Rev. A 43 6990

    [11]

    Wang T, Wang K J, Jia N 2011 Neural Computing 74 1673

    [12]

    Grudzinski K, Zebrowski J J 2004 Physica A 336 153

    [13]

    Budd C J, Piiroinenb P T 2006 Physica D 220 127

    [14]

    He D R, Wang B H, Bauer M, Habip S, Krueger U, Martienssen W, Christiansen B 1994 Physica D 79 335

    [15]

    Qu S X, Cristiansen B, He D R 1995 Phys. Lett. A 201 413

    [16]

    Qu S X, Lu Y Z, Zhang L, He D R 2008 Chin. Phys. B 17 4418

    [17]

    Ren H P, Liu D 2005 Chin. Phys. 14 1352

  • [1]

    Kanoke K 1992 Chaos 2 279

    [2]

    Kanoke K 1991 Physica D 54 5

    [3]

    Hu G, Qu Z L 1994 Phys. Rev. Lett. 72 68

    [4]

    Batista A M, Pinto S E de S, Viana R L, Lopes S R 2002 Phys. Rev. E 65 056209

    [5]

    Santos A M,Viana R L, Lopes S R, Pinto S E de S, Batista A M 2006 Physica A 367 145

    [6]

    Yang W M 1994 Spatio-temproal Chaos and Coupled Map Lattices (Shanghai: Education And Technology Press of Shanghai) (in Chinese) [杨维明 1994 时空混沌和耦合映像格子(上海: 上海教育科技出版社)]

    [7]

    Wiesenfeld K, Hadley P 1989 Phys. Rev. Lett. 62 1335

    [8]

    Sompolinsky H, Golomb D 1991 Phys. Rev. A 43 6990

    [9]

    Wiesenfeld K, Bracikowski C, James G, Roy R 1990 Phys. Rev. Lett. 65 1749

    [10]

    Sompolinsky H, Golomb D, Kleinfeld D 1991 Phys. Rev. A 43 6990

    [11]

    Wang T, Wang K J, Jia N 2011 Neural Computing 74 1673

    [12]

    Grudzinski K, Zebrowski J J 2004 Physica A 336 153

    [13]

    Budd C J, Piiroinenb P T 2006 Physica D 220 127

    [14]

    He D R, Wang B H, Bauer M, Habip S, Krueger U, Martienssen W, Christiansen B 1994 Physica D 79 335

    [15]

    Qu S X, Cristiansen B, He D R 1995 Phys. Lett. A 201 413

    [16]

    Qu S X, Lu Y Z, Zhang L, He D R 2008 Chin. Phys. B 17 4418

    [17]

    Ren H P, Liu D 2005 Chin. Phys. 14 1352

  • [1] Wang Kai, Pei Wen-Jiang, Zhang Yi-Feng, Zhou Si-Yuan, Shao Shuo. Parameter estimate from coupled map lattices based on symbolic vector dynamics. Acta Physica Sinica, 2011, 60(7): 070502. doi: 10.7498/aps.60.070502
    [2] Wang Kai, Pei Wen-Jiang, Xia Hai-Shan, He Zhen-Ya. Initial condition estimation from coupled map lattices based on symbolic vector dynamics. Acta Physica Sinica, 2007, 56(7): 3766-3770. doi: 10.7498/aps.56.3766
    [3] Lin Lan-Xin, Li Xiao-Yan, Shen Min-Fen, Chang Chun-Qi. Initial condition estimate of coupled map lattices system based on symbolic dynamics. Acta Physica Sinica, 2009, 58(5): 2921-2929. doi: 10.7498/aps.58.2921
    [4] Peng Xing-Zhao, Yao Hong, Du Jun, Ding Chao, Zhang Zhi-Hao. Study on cascading invulnerability of multi-coupling-links coupled networks based on time-delay coupled map lattices model. Acta Physica Sinica, 2014, 63(7): 078901. doi: 10.7498/aps.63.078901
    [5] Study of initial condition recovery from multi-coupled map lattices. Acta Physica Sinica, 2007, 56(12): 6836-6842. doi: 10.7498/aps.56.6836
    [6] Jiang Pin-Qun, Wang Bing-Hong, Xia Qing-Hua, Bu Shou-Liang. Control of spatio-temporal chaos in coupled map lattices by state feedback. Acta Physica Sinica, 2004, 53(10): 3280-3286. doi: 10.7498/aps.53.3280
    [7] Liu Ying, Shen Min-Fen, Chan Francis H. Y.. Recovery of statistical property of initial conditions based on time-varying parameter from coupled map lattices. Acta Physica Sinica, 2006, 55(2): 564-571. doi: 10.7498/aps.55.564
    [8] Liu Jian-Dong, Yu You-Ming. A TCML-based spatiotemporal chaotic one-way Hash function with changeable-parameter. Acta Physica Sinica, 2007, 56(3): 1297-1304. doi: 10.7498/aps.56.1297
    [9] Ma Xiu-Juan, Zhao Hai-Xing, Hu Feng. Cascading failure analysis in hyper-network based on the hypergraph. Acta Physica Sinica, 2016, 65(8): 088901. doi: 10.7498/aps.65.088901
    [10] Cheng Xing-Chao, Yang Ke-Li, Qu Shi-Xian. Chimera states in a globally coupled discontinuous map lattices. Acta Physica Sinica, 2014, 63(14): 140505. doi: 10.7498/aps.63.140505
  • Citation:
Metrics
  • Abstract views:  1225
  • PDF Downloads:  347
  • Cited By: 0
Publishing process
  • Received Date:  17 May 2011
  • Accepted Date:  25 June 2011
  • Published Online:  15 April 2012

Frozen random patterns in a globally coupled discontinuous map lattices system

  • 1. Institute of Theoretical & Computational Physics, School of Physics and Information Technology, Shaanxi Normal University, Xi’an 710062, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No.10875076), and the Natural Science Foundation of Shaanxi Province (Grant No.SJ08A23).

Abstract: A class of the characteristic collective dynamic behaviors, i.e., the frozen random patterns, in a globally coupled both-discontinuous-and-non-invertible-map lattices are studied. The coupling-strength dependences of the mean order parameters and the largest Lyapunov exponents are calculated and analyzed. The result shows that, given the initial values for the dynamical variables, the system will reach its complete or partial synchronization state when the coupling strength is beyond some critical value, where the frozen random pattern appears. These phenomena reveal that there are coexisting attractors in the system, and thus the structure and the distribution of the frozen random patterns sensitively depend on the choice of the initial dynamics variables. The interesting event is that the system can be modulated to some regular states of motion by the coupling among lattices even when the single maps are in the chaotic states, which may have some important applications in controlling chaos. The rich dynamical behaviors mentioned above are due to the interplay between the discontinuity and the non-invertibility in the map.

Reference (17)

Catalog

    /

    返回文章
    返回