Local Structures of Chaotic Attractors and q-Phase Transitions at Attractor-Merging Crises in the Sine-Circle Maps: General and Mathematical Physics
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概要
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A merging of two coexisting phase-locked chaotic attractors into one phase-unlocked chaotic attractor occurs in the region where two Arnold tongues overlap each other. This merging is studied in terms of a weighted average Λ (q),(-∞< q< ∞) of the coarse-grained local expansion rates Λ of nearby orbits with a q-dependent weight. Just before the merging, each of the two coexisting attractors has local structures similar to that of the attractor of the logistic map F(x) =1-2x^2, and, as q is varied, Λ(q) for each exhibits two discontinuous transitions at q=q_α=2.0 and q=q_β≃0.0. The phase for q_α > q > q_β is dominated by the normal orbits with Λ equal to a positive Liapunov exponent Λ_k, (k=1,2). A theory of the q-phase transitions is proposed. Just after the merging, the phase-unlocked attractor has a singular local structure, and Λ(q) exhibits a new discontinuous transition from Λ_1 to Λ_2 at q=q_γ=1.0 due to the intermittent hopping motions between two repellers with Λ≃Λ_1 and Λ≃ Λ_2. These features of the attractors just before and after the merging are quite universal and can be summarized in terms of linear parts of the expansion-rate spectrum h(Λ).
- 理論物理学刊行会の論文
- 1988-11-25
著者
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HORITA Takehiko
Department of Mathematical Sciences, Osaka Prefecture University
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岡本 寿夫
高知大学理学部情報科学科
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岡本 寿夫
九州大学
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OKAMOTO Hisao
Department of Information Science, Kochi University
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TOMITA Koji
Department of Physics, Kyushu University
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HATA Hiroki
Department of Physics, Kyushu University
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MORITA Terumitsu
Department of Physics, Kyushu University
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MORI Hazime
Depratment of Physics, Kyushu University
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MORITA Terumitsu
Depratment of Physics, Kyushu University
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KUROKI Shoichi
Department of Physics, Kyushu University
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Hata Hiroki
Department Of Pathology Tohoku University Hospital
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Tomita K
Tokyo Development Center Yaskawa Electric Mfg.co. Ltd
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Tomita Koji
Department Of Physics Kyushu University
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Hata H
Kagoshima Univ. Kagoshima
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Tomita K
Yukawa Institute For Theoretical Physics Kyoto University
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Kuroki S
Fukuoka Women's Univ. Fukuoka Jpn
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Kuroki Shoichi
Fukuoka Women's University
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Kuroki Shoichi
Department Of Physics Kyushu University
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Hata Hiroki
Department Of Internal Medicine Cardiovascular Hospital Of Central Japan (kitakanto Cardiovascular H
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Horita Takehiko
Department Of Control Engineering And Science Kyushu Institute Of Technology
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Morita T
Tohoku Univ. Sendai Jpn
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Hata Hiroki
Department Of Clinical Pharmacy Oita University Hospital
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Tomita Kenji
Research Institute For Theoretical Physics Hiroshima Unviersity
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MORITA Terumitu
Department of Physics Kyushu University
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MURAYAMA Toru
Department of Physics, Kyushu University
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HATA Hiroki
Department of Physics, Kagoshima University
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HORITA Takehiko
Department of Physics Kyushu Universuty
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Tomita Koji
Department of Chemistry, School of Science, Tokai University
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TOMITA Koji
Tokyo Development Center Yaskawa Electric MFG.Co.,LTD
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TOMITA Koji
Department of Physics, Kyushu Uniersity
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TOMITA Koji
Department of Chemistry School of Science, Tokai University
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