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Prog. Theor. Phys. Vol. 68 No. 4 (1982) pp. 1105-1121

[ Full Text PDF : FREE ACCESS (692K) ]

Multiperiodic Flows, Chaos and Lyapunov Exponents

Hirokazu Fujisaka

Department of Physics, Kagoshima University, Kagoshima 890

(Received April 30, 1982)

Abstract:

The existence of positive Lyapunov exponents for almost all initial conditions ensures nonperiodic behavior of chaotic flows. In multiperiodic flows responses to external perturbations as well as the stability of an attractor can be expressed in terms of Lyapunov exponents. In the present paper we summarize basic properties of Lyapunov exponents, and influences of external perturbations (deterministric ones, noise and diffusion) on multiperiodic flows are investigated with the aid of Lyapunov exponents. We find a new feature of onset of diffusion-induced turbulence, and a statistical-physical theory is developed in order to clarify its statistical characteristics. Furthermore a theoretical possibility of a new type of diffusion-induced turbulence will be conjectured.


URL : http://ptp.ipap.jp/link?PTP/68/1105/
DOI : 10.1143/PTP.68.1105

[ Full Text PDF : FREE ACCESS (692K) ] Citation:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 69 No. 1 (1983) pp. 32-47 :
    Stability Theory of Synchronized Motion in Coupled-Oscillator Systems
    Hirokazu Fujisaka and Tomoji Yamada
  2. Progress of Theoretical Physics Vol. 70 No. 5 (1983) pp. 1264-1275 :
    Statistical Dynamics Generated by Fluctuations of Local Lyapunov Exponents
    Hirokazu Fujisaka
  3. Progress of Theoretical Physics Vol. 106 No. 2 (2001) pp. 315-322 :
    Possibility of Soft-Mode Turbulence in Reaction-Diffusion Systems
    Hirokazu Fujisaka and Tomoji Yamada

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