HOME    |    BROWSE    |    SEARCH    |    SUBSCRIPTION   |    SUBMISSION    |    REGISTRATION

Quick Search:
Author: Title/Abstract: Vol./No: Page:
PTP Online Top > Volume 69 (1983) > Number 1
| Next Article >

Prog. Theor. Phys. Vol. 69 No. 1 (1983) pp. 32-47

[ Full Text PDF : FREE ACCESS (607K) ]

Stability Theory of Synchronized Motion in Coupled-Oscillator Systems

Hirokazu Fujisaka and Tomoji Yamada*

Department of Physics, Kagoshima University, Kagoshima 890
*Department of Physics, Kyushu Institute of Technology, Kitakyushu 804

(Received July 30, 1982)

Abstract:

The general stability theory of the synchronized motions of the coupled-oscillator systems is developed with the use of the extended Lyapunov matrix approach. We give the explicit formula for a stability parameter of the synchronized state Ψunif. When the coupling strength is weakened, the coupled system may exhibit several types of non-synchronized motion. In particular, if Ψunif is chaotic, we always get a transition from chaotic Ψunif to a certain non-uniform state and finally the non-uniform chaos. Details associated with such transition are investigated for the coupled Lorenz model. As an application of the theory, we propose a new experimental method to directly measure the positive Lyapunov exponent of intrinsic chaos in reaction systems.


URL : http://ptp.ipap.jp/link?PTP/69/32/
DOI : 10.1143/PTP.69.32

[ Full Text PDF : FREE ACCESS (607K) ] Citation:

References:

  1. Y. Kuramoto and T. Yamada, Prog. Theor. Phys. 56 (1976), 679[PTP].
  2. T. Yamada and Y. Kuramoto, Prog. Theor. Phys. 56 (1976), 681[PTP].
  3. H. Fujisaka and T. Yamada, Prog. Theor. Phys. 57 (1977), 734[PTP].
  4. T. Yamada and H. Fujisaka, Z. Phys. B 28 (1977), 239.
  5. T. Yamada and H. Fujisaka, Prog. Theor. Phys. Suppl. No. 64 (1978), 269[PTP].
  6. Y. Kuramoto, Prog. Theor. Phys. Suppl. No. 64 (1978), 346[PTP].
  7. H. Fujisaka and T. Yamada, Z. Phys. B 37 (1980), 265.
  8. Y. Kuramoto, Physica A 106 (1981), 128[CrossRef].
  9. J. P. Gollub, E. J. Romer and J. E. Socolar, J. Stat. Phys. 23 (1980), 321.
  10. T. Yamada, J. Phys. Soc. Jpn. 51 (1982), 3423[JPSJ].
  11. H. Fujisaka, Prog. Theor. Phys. 68 (1982), 1105[PTP].
  12. E. N. Lorenz, J. Atmos. Sci. 20 (1963), 130.
  13. G. Benettin, L. Galgani and J. Strelcyn, Phys. Rev. A 14 (1976), 2338[APS].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 67 (1998) pp. 3055-3060 :
    Synchronized Chaos in Heterogeneous Systems [rf:99]
    Daisuke Katsuragi
  2. Journal of the Physical Society of Japan 69 (2000) pp. 1-4 :
    Edge of Chaos in Stochastically Coupled Cellular Automata
    Masayoshi Inoue and Masakazu Nagadome
  3. Journal of the Physical Society of Japan 70 (2001) pp. 3189-3192 :
    Nonperturbative Analysis of Chaos Synchronization in Coupled Logistic Maps
    Yutaka Nishi, Ayumi Setoyama and Masayoshi Inoue
  4. Journal of the Physical Society of Japan 74 (2005) pp. 1645-1648 :
    Synchronization of Chaotic Fractional Chen System
    Weihua Deng and Changpin Li
  5. Journal of the Physical Society of Japan 75 (2006) 094801 (6 pages) :
    Projective-Lag Synchronization of Coupled Multidelay Feedback Systems
    Thang Manh Hoang and Masahiro Nakagawa
  6. Journal of the Physical Society of Japan 76 (2007) 093002 (3 pages) :
    A New Approach to Synchronization of Discrete-Time Chaotic Systems
    Ju Hyun Park
  7. Progress of Theoretical Physics Vol. 70 No. 5 (1983) pp. 1240-1248 :
    Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. II
    Tomoji Yamada and Hirokazu Fujisaka
  8. Progress of Theoretical Physics Vol. 70 No. 5 (1983) pp. 1264-1275 :
    Statistical Dynamics Generated by Fluctuations of Local Lyapunov Exponents
    Hirokazu Fujisaka
  9. Progress of Theoretical Physics Vol. 72 No. 5 (1984) pp. 885-894 :
    Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. III
    Tomoji Yamada and Hirokazu Fujisaka
  10. Progress of Theoretical Physics Vol. 74 No. 4 (1985) pp. 918-921 :
    A New Intermittency in Coupled Dynamical Systems
    Hirokazu Fujisaka and Tomoji Yamada
  11. Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1087-1104 :
    Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. IV
    Hirokazu Fujisaka and Tomoji Yamada
  12. Progress of Theoretical Physics Vol. 92 No. 3 (1994) pp. 509-519 :
    Transitions to Defect Turbulence in an Anisotropic System
    Hidetsugu Sakaguchi
  13. Progress of Theoretical Physics Vol. 94 No. 4 (1995) pp. 515-534 :
    Nearly Synchronized State and a Constant of Motion in a Coupled Chaotic Map
    Masayoshi Inoue and Yutaka Nishi
  14. Progress of Theoretical Physics Vol. 97 No. 3 (1997) pp. 387-398 :
    Appearance of an Invariant Manifold and On-Off Intermittency in Coupled-Maps
    Masayoshi Inoue, Takashi Kawazoe and Hiroki Hata
  15. Progress of Theoretical Physics Vol. 105 No. 2 (2001) pp. 187-196 :
    New Riddling Bifurcation in Asymmetric Dynamical Systems
    Sang-Yoon Kim, Woochang Lim and Youngtae Kim
  16. Progress of Theoretical Physics Vol. 107 No. 2 (2002) pp. 239-252 :
    Effect of Parameter Mismatch and Noise on Weak Synchronization
    Sang-Yoon Kim, Woochang Lim and Youngtae Kim
  17. Progress of Theoretical Physics Vol. 108 No. 6 (2002) pp. 999-1019 :
    Extended Self-Similarity in Modulational Intermittency Based on the Continuous-Time Random Walk Approach
    Syuji Miyazaki and Kei Ito
  18. Progress of Theoretical Physics Vol. 114 No. 2 (2005) pp. 289-299 :
    Mapping Model of Chaotic Phase Synchronization
    Hirokazu Fujisaka, Satoki Uchiyama and Takehiko Horita
  19. Progress of Theoretical Physics Vol. 116 No. 5 (2006) pp. 819-837 :
    Stochastic Model of Chaotic Phase Synchronization. I
    Tomoji Yamada, Takehiko Horita, Katsuya Ouchi and Hirokazu Fujisaka
  20. Progress of Theoretical Physics Vol. 123 No. 6 (2010) pp. 923-939 :
    Various Synchronization Phenomena in Discrete-Time Coupled Chaotic Rotors
    Kai Morino, Takehiko Horita and Syuji Miyazaki
  21. Progress of Theoretical Physics Supplement No.99 (1989) pp. 120-130 :
    A New Type of Intermittency in an Electronic Circuit
    Tomoji Yamada, Kazuhiro Fukushima and Taichi Yazaki
  22. Progress of Theoretical Physics Supplement No.139 (2000) pp. 164-177 :
    Chaotic Synchronization between Coupled Pancreatic β-Cells
    Brian Lading, Erik Mosekilde, Sergiy Yanchuk and Yuri Maistrenko
  23. Progress of Theoretical Physics Supplement No.161 (2006) pp. 340-343 :
    Detecting Generalized Synchronization of Chaotic Dynamical Systems
    Hiromichi Suetani, Yukito Iba and Kazuyuki Aihara
  24. Progress of Theoretical Physics Supplement No.161 (2006) pp. 352-355 :
    Convective Stabilization of Saddle Fixed Points in an Open Flow System
    Masashi Tachikawa

[PTP HOME] [BROWSE] [SEARCH] [SUBSCRIPTION] [SUBMISSION] [REGISTRATION]

Copyright © Progress of Theoretical Physics 2013 All rights reserved.