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Prog. Theor. Phys. Vol. 61 No. 3 (1979) pp. 825-841

[ Full Text PDF : FREE ACCESS (1060K) ]

Thermal Fluctuation of a Self-Oscillating Reaction System Entrained by a Periodic External Force

Hiroaki Daido and Kazuhisa Tomita

Department of Physics, Kyoto University, Kyoto 606

(Received October 17, 1978)

Abstract:

The thermal fluctuation of a self-oscillating system entrained by a periodic external force is studied by means of the system size expansion method with the aid of the reductive perturbation approach. Three main results are obtained, i.e., (i) the suppression of the ensemble dephasing or phase diffusion of a free limit cycle by a periodic force (ii) the critical anomaly of the fluctuations at the instability points of the entrained system (iii) the existence of the stroboscopic circulation of fluctuation which is defined analogously to the irreversible circulation of fluctuation and plays the central role in characterizing the instabilities of the entrained system. These results do not depend on particular models although the Sel'kov-Higgins model for the glycolytic reaction is used in the present work.


URL : http://ptp.ipap.jp/link?PTP/61/825/
DOI : 10.1143/PTP.61.825

[ Full Text PDF : FREE ACCESS (1060K) ] Citation:

References:

  1. For example. P. Glandsdorff and I. Prigogine, Thermodynamic Theory of Structure, Stability and Fluctuation (Wiley-Interscience, 1971).
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    See also 1) and 2).
  11. N. Minorsky, Non-linear Oscillations (von Nostrand, 1962).
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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 62 No. 6 (1979) pp. 1519-1532 :
    Thermal Fluctuation of a Self-Oscillating Reaction System under a Periodic External Force. II
    Hiroaki Daido and Kazuhisa Tomita
  2. Progress of Theoretical Physics Vol. 66 No. 2 (1981) pp. 385-405 :
    Control and Dissipation in Oscillatory Chemical Engines
    Peter H. Richter, Paul Rehmus and John Ross
  3. Progress of Theoretical Physics Vol. 73 No. 3 (1985) pp. 638-648 :
    Random Frequency Modulation of a Forced Nonlinear Oscillator
    Yoshiki Kuramoto and Shigeru Shinomoto
  4. Progress of Theoretical Physics Supplement No.79 (1984) pp. 75-95 :
    Coupling Sensitivity of Chaos
    Hiroaki Daido

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