Prog. Theor. Phys. Vol. 79 No. 3 (1988) pp. 581-599
Global Spectral Structures of Type III Intermittent Chaos
Department of Physics, Kyushu University 33, Fukuoka 812
(Received September 28, 1987)
Power spectra of type III intermittent chaos near its onset point are investigated by developing a statistical-physical theory of power spectra of intermittent chaos due to Mori et al. It is shown that the power spectra exhibit eminent peaks at selected frequencies m ω0 with m = 0, 1/2, 1, 3/2, 2, …, where ω0 is an eigenfrequency of laminar oscillations. The peaks at nonzero integers are produced by the laminar oscillations with frequency ω0 and higher harmonics, as has been investigated in type I intermittent chaos, whereas the peaks at half integers are generated by the inverted period-doubling bifurcation. The shapes of these peaks are characterized by the fluctuations of durations and amplitude modulations of the laminar oscillations and by the random jumps of their phase shifts by bursts. Thus it turns out that the shape of each peak obeys an inverse-power law 1/|ω- m ω0|ζm with a universal exponent ζm, where ζm = 1/2 if m is 0 or a half integer and ζm = 3/2 if m is an integer, and there exists a small saturation frequency which tends to zero as the onset point is approached.
DOI : 10.1143/PTP.79.581
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Citing Article(s) :
Journal of the Physical Society of Japan 57 (1988) pp. 4055-4062
Type-III Intermittency in a Coupled Nonlinear LCR Circuit
Kazuhiro Fukushima and Tomoji Yamada
Progress of Theoretical Physics Vol. 81 No. 1 (1989) pp. 60-77
Scaling Structures and Statistical Mechanics of Type I Intermittent Chaos
Nobuyuki Mori, Tatsuharu Kobayashi, Hiroki Hata, Terumitsu Morita, Takehiko Horita and Hazime Mori
Progress of Theoretical Physics Supplement No.99 (1989) pp. 1-63
Statistical Mechanics of Dynamical Systems
Hazime Mori, Hiroki Hata, Takehiko Horita and Tatsuharu Kobayashi