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Prog. Theor. Phys. Vol. 80 No. 5 (1988) pp. 793-808

[ Full Text PDF : FREE ACCESS (807K) ]

Local Structures of Chaotic Attractors and q-Phase Transitions at Attractor-Merging Crises in the Sine-Circle Maps

Takehiko Horita, Hiroki Hata, Hazime Mori, Terumitsu Morita, Koji Tomita, Shoichi Kuroki and Hisao Okamoto

Department of Physics, Kyushu University 33, Fukuoka 812

(Received March 2, 1988)

Abstract:

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)=1-2x2, and as q is varied, Λ(q) for each exhibits two discontinuous transitions at q=qα=2.0 and q=qβ≃0.0. The phase for qα>q>qβ is dominated by the normal orbits with Λ equal to a positive Liapunov exponent Λk, (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 Λ1 to Λ2 at q=qγ=1.0 due to the intermittent hopping motions between two repellers with Λ≃Λ1 and Λ≃Λ2. 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).


URL : http://ptp.ipap.jp/link?PTP/80/793/
DOI : 10.1143/PTP.80.793

[ Full Text PDF : FREE ACCESS (807K) ] Citation:

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  13. Progress of Theoretical Physics Vol. 83 No. 4 (1990) pp. 649-654 :
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  14. Progress of Theoretical Physics Vol. 84 No. 1 (1990) pp. 18-22 :
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  16. Progress of Theoretical Physics Vol. 84 No. 4 (1990) pp. 558-562 :
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  17. Progress of Theoretical Physics Vol. 91 No. 4 (1994) pp. 677-692 :
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  18. Progress of Theoretical Physics Vol. 102 No. 6 (1999) pp. 1057-1064 :
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