Prog. Theor. Phys. Vol. 69 No. 6 (1983) pp. 1806-1810

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Letters

Doubling of Torus

Kunihiko Kaneko

Department of Physics, University of Tokyo, Tokyo 113

(Received March 11, 1983)

Abstract:

“Doubling of torus” is found in three-or four-dimensional dissipative mappings. In these models, doubling occurs only a finite number of times before chaos appears. An explanation is attempted by a numerical study on the stability against perturbation of the direct product state of coupled logistic and torus maps.

URL : http://ptp.ipap.jp/link?PTP/69/1806/
DOI : 10.1143/PTP.69.1806

References:

D. Ruelle and F. Takens, Commun. Math. Phys. 20 (1971), 167[CrossRef].
S. J. Shenker, Physica D 5 (1982), 405[CrossRef].
L. Glass and R. Perez, Phys. Rev. Lett. 48 (1982), 1772[APS].
K. Kaneko, Prog. Theor. Phys. 68 (1982), 669[PTP].
M. J. Feigenbaum, L. P. Kadanoff and S. J. Shenker, Physica D 5 (1982), 370[CrossRef].
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K. Kaneko, Prog. Theor. Phys. 69 (1983), 403[PTP].
L. P. Kadanoff, Preprint (1983).
K. Kaneko, Prog. Theor. Phys. 69 (1983), 1427[PTP].
K. Kaneko, in preparation.
M. Sano and Y. Sawada, Preprint (1982).
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See also M. Lücke and Y. Saito, Phys. Lett. A 91 (1982), 205 [CrossRef]for the logistic map with commensurate parametric modulation.
J. P. Crutchfield and B. A. Huberman, Phys. Lett. A 74 (1980), 407[CrossRef].
For the case of noisy period-doubling, see J. P. Crutchfield, M. Nauenberg and J. Rudnick, Phys. Rev. Lett. 46 (1981), 933[APS].
G. Shraiman, C. E. Wayne and P. C. Martin, Phys. Rev. Lett. 46 (1981), 935[APS].
M. J. Feigenbaum and B. Hasslacher, Phys. Rev. Lett. 49 (1982), 605[APS].

Citing Article(s) :

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
Progress of Theoretical Physics Vol. 71 No. 2 (1984) pp. 282-294 :
Fates of Three-Torus. I

Kunihiko Kaneko
Progress of Theoretical Physics Vol. 71 No. 2 (1984) pp. 402-405 :
Onset of Intermittency from Torus

Hiroaki Daido
Progress of Theoretical Physics Vol. 71 No. 5 (1984) pp. 1112-1115 :
Fractalization of Torus

Kunihiko Kaneko
Progress of Theoretical Physics Vol. 72 No. 2 (1984) pp. 202-215 :
Oscillation and Doubling of Torus

Kunihiko Kaneko
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
Progress of Theoretical Physics Vol. 72 No. 6 (1984) pp. 1089-1103 :
Supercritical Behavior of Disordered Orbits of a Circle Map

Kunihiko Kaneko