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Prog. Theor. Phys. Vol. 72 No. 2 (1984) pp. 202-215

[ Full Text PDF : FREE ACCESS (833K) ]

Oscillation and Doubling of Torus

Kunihiko Kaneko

Department of Physics, University of Tokyo, Tokyo 113

(Received February 20, 1984)

Abstract:

Two features of the instability of torus along the amplitude direction are investigated, using various two-dimensional mappings. First, the oscillation of a torus in a delayed logistic map is studied, which is related with the oscillation of an unstable manifold of a periodic saddle. The oscillation is also analyzed from another point of view, i.e., the synergetic effect of the rotation, stretching and folding, which is typically seen in the delayed piecewise-linear mapping. Critical phenomena after the onset of chaos are also discussed. Second, the doubling of a torus is reinvestigated. A torus doubling occurs only a finite number of times. The mechanism of the interruption of the doubling is discussed from three points of view, i.e., relevant perturbation in the RG framework, fractalization and the intermittent-like bursts between the valleys of the multi-humped mapping.


URL : http://ptp.ipap.jp/link?PTP/72/202/
DOI : 10.1143/PTP.72.202

[ Full Text PDF : FREE ACCESS (833K) ] Citation:

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Citing Article(s) :

  1. 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
  2. Progress of Theoretical Physics Vol. 71 No. 2 (1984) pp. 282-294 :
    Fates of Three-Torus. I
    Kunihiko Kaneko
  3. Progress of Theoretical Physics Vol. 72 No. 6 (1984) pp. 1089-1103 :
    Supercritical Behavior of Disordered Orbits of a Circle Map
    Kunihiko Kaneko
  4. Progress of Theoretical Physics Vol. 76 No. 1 (1986) pp. 302-304 :
    Oscillations of Torus and Collision Torus-Chaos in a Delayed Circle Map
    Claudio Franciosi
  5. Progress of Theoretical Physics Vol. 87 No. 1 (1992) pp. 1-60 :
    Collective Behaviors in Spatially Extended Systems with Local Interactions and Synchronous Updating
    Hugues Chaté and Paul Manneville
  6. Progress of Theoretical Physics Vol. 121 No. 4 (2009) pp. 671-683 :
    Strange Nonchaotic Responses of the Quasiperiodically Forced Morris-Lecar Neuron
    Woochang Lim, Sang-Yoon Kim and Youngtae Kim

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