Prog. Theor. Phys. Vol. 68 No. 6 (1982) pp. 1864-1879

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Global Aspects of the Dissipative Dynamical Systems. II

— Periodic and Chaotic Responses in the Forced Lorenz System —

Yoji Aizawa and Tatsuya Uezu

Department of Physics, Kyoto University, Kyoto 606

(Received June 7, 1982)

Abstract:

The response of the chaotic motion under a periodic perturbation is studied using the Lorenz model. The global phase diagram is obtained by computer simulations. The periodic response is characterized not only by the subharmonic frequency but also by the symmetry of the orbit in phase space. On the other hand, the chaotic response is characterized by two chaos parameters: fractal dimensions of the strange attractor and of the symbolic time series.
The periodic perturbation induces a partially coherent response which is closely connected with the temporal intermittency appearing in the time series of the dynamical variables. Such a coherent behavior is understood in terms of the spectral analysis, fractal dimensions and the information entropy.

URL : http://ptp.ipap.jp/link?PTP/68/1864/
DOI : 10.1143/PTP.68.1864

References:

Y. Aizawa, Prog. Theor. Phys. 68 (1982), 64[PTP].
This paper is referred to as paper I in the text.
A. H. Nayfeh and D. T. Mook; Nonlinear Oscillation (John Wiley and Sons, N. Y., 1979).
E. N. Lorenz, J. Atm. Sci. 20 (1963), 130.
O. E. Rössler, Z. Naturforsch. 31a (1976), 1664.
An exactly solvable model is discussed in:
(i) Sh. Ito, H. Nakada and S. Tanaka, Tokyo J. Math. 2 (1979), 222; ibid. 2 (1979), 241,
and the statistical aspect near the band merging point is studied in:
(ii) S. J. Shenker and L. Kadanoff, J. of Phys. A 14 (1981), L23[CrossRef].
M. Hénon, Commun. Math. Phys. 50 (1976), 69[CrossRef].
Y. Aizawa, RIMS Kokyuroku (Research Inst. Math. Sci., Kyoto University) 439 (1981), 63.
H. Mori, Prog. Theor. Phys. 63 (1980), 1044[PTP].
D. Rolfsen, Kots and Links (Publish or Perish, Inc., Berkeley, 1976).
Y. Aizawa and T. Uezu, Prog. Theor. Phys. 67 (1982), 982[PTP].
T. Uezu and Y. Aizawa, Prog. Theor. Phys. 68 (1982), 1543[PTP].
T. Uezu, to appear in Phys. Lett. A.
D. Farmer, J. Crutchfield, H. Froeling, N. Packard and R. Show, Annals of the NYAS 375 (1980), 453.
T. Uezu and Y. Aizawa, Prog. Theor. Phys. 68 (1982), 1907[PTP].

Citing Article(s) :

Progress of Theoretical Physics Vol. 68 No. 5 (1982) pp. 1543-1560 :
Some Routes to Chaos from Limit Cycle in the Forced Lorenz System

Tatsuya Uezu and Yoji Aizawa
Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 333-337 :
Intermittency Associated with the Breakdown of the Chaos Symmetry

Hirokazu Fujisaka, Hiroshi Kamifukumoto and Masayoshi Inoue
Progress of Theoretical Physics Vol. 70 No. 3 (1983) pp. 879-882 :
Resonance and Intermittent Transition from Torus to Chaos in Periodically Forced Systems near Intermittency Threshold

Hiroaki Daido
Progress of Theoretical Physics Vol. 70 No. 5 (1983) pp. 1249-1263 :
Symbolic Dynamics Approach to Intermittent Chaos

Yoji Aizawa
Progress of Theoretical Physics Vol. 77 No. 6 (1987) pp. 1344-1354 :
Breakdown of Chaos Symmetry and Intermittency in Band-Splitting Phenomena

Hiroshi Uchimura, Hirokazu Fujisaka and Masaoshi Inoue
Progress of Theoretical Physics Vol. 112 No. 5 (2004) pp. 785-796 :
Global Dynamics in the Periodically Forced Chen System

Debin Huang
Progress of Theoretical Physics Supplement No.79 (1984) pp. 96-124 :
Statistical Mechanics of Intermittent Chaos

Yoji Aizawa, Chikara Murakami and Tamotsu Kohyama