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Prog. Theor. Phys. Vol. 69 No. 5 (1983) pp. 1427-1442

[ Full Text PDF : FREE ACCESS (613K) ]

Transition from Torus to Chaos Accompanied by Frequency Lockings with Symmetry Breaking

— In Connection with the Coupled-Logistic Map —

Kunihiko Kaneko

Department of Physics, University of Tokyo, Tokyo 113

(Received December 18, 1982)

Abstract:

Transition from torus to chaos is studied using the coupled-logistic map. We observe the period-adding sequence, which obeys the critical phenomena of a one-dimensional mapping. The fixed Lyapunov exponent is also obtained. The locking that appears after the sequence breaks the symmetry of the system. Self-similar stripe structure of basins is also found. Various properties and a phase diagram of the map are given. The mechanism of the distortion of torus and transition to chaos is also discussed.


URL : http://ptp.ipap.jp/link?PTP/69/1427/
DOI : 10.1143/PTP.69.1427

[ Full Text PDF : FREE ACCESS (613K) ] Citation:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 59 (1990) pp. 1123-1126 :
    Self-Similar Structures in the Phase Diagram of a Coupled-Logistic Map
    Kazuhiro Satoh and Takashi Aihara
  2. Journal of the Physical Society of Japan 59 (1990) pp. 1184-1198 :
    Numerical Study on a Coupled-Logistic Map as a Simple Model for a Predator-Prey System
    Kazuhiro Satoh and Takashi Aihara
  3. Journal of the Physical Society of Japan 60 (1991) pp. 718-719 :
    Quasiperiodic Route to Chaosin a Coupled Logistic Map
    Kazuhiro Satoh
  4. Journal of the Physical Society of Japan 60 (1991) pp. 1533-1540 :
    Numerical Study on a Coupled Logistic Map as a Simple Model for Three Competing Species
    Kazuhiro Satoh
  5. Journal of the Physical Society of Japan 62 (1993) pp. 497-505 :
    Bifurcations of the Complex Dynamical System Zn+1=ln (Zn)+C
    Takeshi Kawabe and Yoshiro Kondo
  6. Journal of the Physical Society of Japan 62 (1993) pp. 3767-3770 :
    Critical Behavior of Complex Logarithmic Map
    Masaaki Tanaka and Takeshi Kawabe
  7. Progress of Theoretical Physics Vol. 69 No. 6 (1983) pp. 1806-1810 :
    Doubling of Torus
    Kunihiko Kaneko
  8. 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
  9. Progress of Theoretical Physics Vol. 71 No. 1 (1984) pp. 35-49 :
    Fractal Basin Structure
    Shinji Takesue and Kunihiko Kaneko
  10. Progress of Theoretical Physics Vol. 71 No. 2 (1984) pp. 282-294 :
    Fates of Three-Torus. I
    Kunihiko Kaneko
  11. Progress of Theoretical Physics Vol. 71 No. 5 (1984) pp. 1112-1115 :
    Fractalization of Torus
    Kunihiko Kaneko
  12. Progress of Theoretical Physics Vol. 72 No. 2 (1984) pp. 202-215 :
    Oscillation and Doubling of Torus
    Kunihiko Kaneko
  13. Progress of Theoretical Physics Vol. 72 No. 3 (1984) pp. 480-486 :
    Period-Doubling of Kink-Antikink Patterns, Quasiperiodicity in Antiferro-Like Structures and Spatial Intermittency in Coupled Logistic Lattice
    Kunihiko Kaneko
  14. Progress of Theoretical Physics Vol. 72 No. 4 (1984) pp. 853-856 :
    Coupling Sensitivity of Chaos
    Hiroaki Daido
  15. 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
  16. Progress of Theoretical Physics Vol. 77 No. 6 (1987) pp. 1307-1318 :
    Oregonator Model with a Flow Term for the Belousov-Zhabotinskii Reaction Having Constant Feed. I
    Chiaki Murase, Shinji Sakanoue and Mitsuo Endo
  17. Progress of Theoretical Physics Vol. 78 No. 2 (1987) pp. 305-315 :
    Bifurcations of the Coupled Logistic Map
    Hidetsugu Sakaguchi and Kazuhisa Tomita
  18. Progress of Theoretical Physics Vol. 88 No. 4 (1992) pp. 769-773 :
    Solving an Optimization Problem with a Chaos Neural Network
    Masayoshi Inoue and Akihiro Nagayoshi
  19. Progress of Theoretical Physics Vol. 94 No. 4 (1995) pp. 571-575 :
    Folded Bifurcation in Coupled Asymmetric Logistic Maps
    Shoichi Midorikawa, Takayuki Kubo and Taksu Cheon
  20. Progress of Theoretical Physics Vol. 106 No. 1 (2001) pp. 17-37 :
    Universal Bicritical Behavior of Period Doublings in Unidirectionally Coupled Oscillators
    Sang-Yoon Kim, Woochang Lim and Youngtae Kim
  21. Progress of Theoretical Physics Supplement No.79 (1984) pp. 75-95 :
    Coupling Sensitivity of Chaos
    Hiroaki Daido

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