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Prog. Theor. Phys. Vol. 71 No. 3 (1984) pp. 513-523

[ Full Text PDF : FREE ACCESS (592K) ]

Theory of Diffusion and Intermittency in Chaotic Systems

Hirokazu Fujisaka

Department of Physics, Kagoshima University, Kagoshima 890

(Received November 25, 1983)

Abstract:

The statistical-dynamics of At obeying At+1 = B(xt)At is investigated, where B is a certain function of xt generated by a chaotic one-dimensional map xt+1 = f(xt). It is shown that At has two complementary aspects, i.e., diffusion and intermittency, reflecting the log-normal and the non-log-normal characteristics of At and governing the low-order statistics of At and the higher-order one, respectively. In order to single out the long-time characteristics of the dynamics we introduce the characteristic exponent, which turns out to be important in describing the above two aspects in a clear-cut way. Interrelation between the characteristic exponent and the probability distribution is briefly discussed. Furthermore, some solvable examples are analyzed as illustrations.


URL : http://ptp.ipap.jp/link?PTP/71/513/
DOI : 10.1143/PTP.71.513

[ Full Text PDF : FREE ACCESS (592K) ] Citation:

References:

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Citing Article(s) :

  1. Journal of the Physical Society of Japan 59 (1990) pp. 2659-2666 :
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  2. Progress of Theoretical Physics Vol. 72 No. 1 (1984) pp. 23-32 :
    Scaling Behaviors of Characteristic Exponents near Chaotic Transition Points
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  3. Progress of Theoretical Physics Vol. 74 No. 1 (1985) pp. 20-30 :
    Theory of Diffusion and Intermittency in Chaotic Systems. II
    Hirokazu Fujisaka and Masayoshi Inoue
  4. Progress of Theoretical Physics Vol. 75 No. 5 (1986) pp. 1087-1104 :
    Stability Theory of Synchronized Motion in Coupled-Oscillator Systems. IV
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  5. Progress of Theoretical Physics Vol. 77 No. 1 (1987) pp. 1-5 :
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    Shinichi Sato, Masaki Sano and Yasuji Sawada
  6. Progress of Theoretical Physics Vol. 77 No. 5 (1987) pp. 1045-1056 :
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    Hirokazu Fujisaka and Tomoji Yamada
  7. Progress of Theoretical Physics Vol. 77 No. 5 (1987) pp. 1077-1089 :
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  8. Progress of Theoretical Physics Vol. 77 No. 6 (1987) pp. 1334-1343 :
    Statistical-Thermodynamics Formalism of Self-Similarity
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  9. Progress of Theoretical Physics Vol. 77 No. 6 (1987) pp. 1344-1354 :
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  10. Progress of Theoretical Physics Vol. 78 No. 2 (1987) pp. 268-281 :
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  11. Progress of Theoretical Physics Vol. 78 No. 6 (1987) pp. 1203-1208 :
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  12. Progress of Theoretical Physics Vol. 79 No. 1 (1988) pp. 1-6 :
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  13. Progress of Theoretical Physics Vol. 79 No. 2 (1988) pp. 296-312 :
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  14. Progress of Theoretical Physics Vol. 79 No. 3 (1988) pp. 557-560 :
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  16. Progress of Theoretical Physics Vol. 79 No. 6 (1988) pp. 1251-1254 :
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  17. Progress of Theoretical Physics Vol. 80 No. 4 (1988) pp. 588-593 :
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  18. Progress of Theoretical Physics Vol. 80 No. 5 (1988) pp. 793-808 :
    Local Structures of Chaotic Attractors and q-Phase Transitions at Attractor-Merging Crises in the Sine-Circle Maps
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  19. Progress of Theoretical Physics Vol. 80 No. 5 (1988) pp. 809-826 :
    Characterization of Local Structures of Chaotic Attractors in Terms of Coarse-Grained Local Expansion Rates
    Hiroki Hata, Takehiko Horita, Hazime Mori, Terumitsu Morita and Koji Tomita
  20. Progress of Theoretical Physics Vol. 80 No. 6 (1988) pp. 923-928 :
    Singular Local Structures of Chaotic Attractors Due to Collisions with Unstable Periodic Orbits in Two-Dimensional Maps
    Takehiko Horita, Hiroki Hata, Hazime Mori Terumitsu Morita and Koji Tomita
  21. Progress of Theoretical Physics Vol. 80 No. 6 (1988) pp. 953-972 :
    Scaling Structures of Chaotic Attractors and q-Phase Transitions at Crises in the Hénon and the Annulus Maps
    Koji Tomita, Hiroki Hata, Takehiko Horita, Hazime Mori and Terumitsu Morita
  22. Progress of Theoretical Physics Vol. 81 No. 1 (1989) pp. 1-6 :
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    Koji Tomita, Hiroki Hata, Takehiko Horita, Hazime Mori and Terumitsu Morita
  23. Progress of Theoretical Physics Vol. 81 No. 1 (1989) pp. 11-16 :
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  24. 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
  25. Progress of Theoretical Physics Vol. 81 No. 6 (1989) pp. 1073-1078 :
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    Takehiko Horita, Hiroki Hata, Hazime Mori and Koji Tomita
  26. Progress of Theoretical Physics Vol. 81 No. 6 (1989) pp. 1124-1134 :
    q-Phase Transitions in Chaotic Attractors of Differential Equations at Bifurcation Points
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  27. Progress of Theoretical Physics Vol. 81 No. 6 (1989) pp. 1135-1145 :
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  28. Progress of Theoretical Physics Vol. 81 No. 6 (1989) pp. 1146-1157 :
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  29. Progress of Theoretical Physics Vol. 82 No. 1 (1989) pp. 1-6 :
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  30. Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 863-868 :
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  31. Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 879-896 :
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  32. Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 897-910 :
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  33. Progress of Theoretical Physics Vol. 83 No. 1 (1990) pp. 22-28 :
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  34. Progress of Theoretical Physics Vol. 84 No. 5 (1990) pp. 824-836 :
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  35. Progress of Theoretical Physics Vol. 85 No. 2 (1991) pp. 187-204 :
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  36. Progress of Theoretical Physics Supplement No.99 (1989) pp. 1-63 :
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  37. Progress of Theoretical Physics Supplement No.99 (1989) pp. 64-81 :
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  38. Progress of Theoretical Physics Supplement No.99 (1989) pp. 82-94 :
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