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Prog. Theor. Phys. Vol. 69 No. 2 (1983) pp. 403-414

[ Full Text PDF : FREE ACCESS (538K) ]

Similarity Structure and Scaling Property of the Period-Adding Phenomena

Kunihiko Kaneko

Department of Physics, University of Tokyo, Tokyo 113

(Received September 8, 1982)

Abstract:

Period-adding sequence at the locking from torus to chaos is studied with the use of a one-dimensional mapping. Similarity and various scaling properties of each cycle are found numerically, which can be explained through a “phenomenological theory” based on the existence of the fixed point function. We classify the sequence into three cases. We also apply our theory to the case in which the sequence is a window among chaotic states.


URL : http://ptp.ipap.jp/link?PTP/69/403/
DOI : 10.1143/PTP.69.403

[ Full Text PDF : FREE ACCESS (538K) ] 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 62 (1993) pp. 497-505 :
    Bifurcations of the Complex Dynamical System Zn+1=ln (Zn)+C
    Takeshi Kawabe and Yoshiro Kondo
  4. Journal of the Physical Society of Japan 62 (1993) pp. 3767-3770 :
    Critical Behavior of Complex Logarithmic Map
    Masaaki Tanaka and Takeshi Kawabe
  5. Progress of Theoretical Physics Vol. 69 No. 5 (1983) pp. 1427-1442 :
    Transition from Torus to Chaos Accompanied by Frequency Lockings with Symmetry Breaking
    Kunihiko Kaneko
  6. Progress of Theoretical Physics Vol. 69 No. 6 (1983) pp. 1806-1810 :
    Doubling of Torus
    Kunihiko Kaneko
  7. Progress of Theoretical Physics Vol. 71 No. 1 (1984) pp. 35-49 :
    Fractal Basin Structure
    Shinji Takesue and Kunihiko Kaneko
  8. Progress of Theoretical Physics Vol. 71 No. 2 (1984) pp. 282-294 :
    Fates of Three-Torus. I
    Kunihiko Kaneko
  9. Progress of Theoretical Physics Vol. 71 No. 3 (1984) pp. 499-512 :
    Self-Similar Cascades of Band Splittings of Linear Mod 1 Maps
    Hazime Mori, Hisao Okamoto and Matsuyuki Ogasawara
  10. Progress of Theoretical Physics Vol. 71 No. 5 (1984) pp. 930-937 :
    Scenarios Leading to Chaos in a Forced Lotka-Volterra Model
    Masayoshi Inoue and Hiroshi Kamifukumoto
  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. 6 (1984) pp. 1089-1103 :
    Supercritical Behavior of Disordered Orbits of a Circle Map
    Kunihiko Kaneko
  15. Progress of Theoretical Physics Vol. 74 No. 5 (1985) pp. 1033-1044 :
    Spatiotemporal Intermittency in Coupled Map Lattices
    Kunihiko Kaneko
  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. 84 No. 1 (1990) pp. 72-80 :
    Novel Scaling in Sine Circle Map
    Tatsuya Uezu and Peter C. Davis

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