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Prog. Theor. Phys. Vol. 57 No. 6 (1977) pp. 1874-1885

[ Full Text PDF : FREE ACCESS (1068K) ]

Nonlinear Fluctuations Associated with Instabilities in Dissipative Systems

Ki-ichi Nakamura

Central Research Laboratories, Nippon Electric Co. Ltd., Kawasaki 213

(Received November 25, 1976)

Abstract:

Computer experiments are performed on a model system of coupled mode equations designed to represent the Gunn instability, in order to investigate the origin of anomalously large fluctuations observed often over a wide range beyond an instability point in a dissipative system. The experiments deal with a system of 40 modes which possesses a number of steady states (attractors) beyond the instability point. It is shown that the system travels in phase space along an erratic or chaotic trajectory for long time in the approach to one of these attractors from an unstable equilibrium point. According to the modern ergodic theory, trajectories are proved to be stochastic by demonstrating that they satisfy the exponential law of growth of stochastic instability, that is, they are unstable with respect to small disturbances. The system provides an example of rigidly deterministic systems whose dynamics are best described in stochastic terms. It is found that under the influence of random forces the system escapes from the reached attractor after fluctuating around it for some time and travels again along a long-lived stochastic trajectory. The system wanders erratically from attractor to attractor via macroscopically stochastic trajectories, which do not arise from external random forces, but from the nonlinearity inherent in the system. This wandering motion is observed as large fluctuations.


URL : http://ptp.ipap.jp/link?PTP/57/1874/
DOI : 10.1143/PTP.57.1874

[ Full Text PDF : FREE ACCESS (1068K) ] Citation:

References:

  1. E. R. Pike, D. A. Jackson, P. J. Bourke and D. I. Page, J. Phys. E 1 (1968), 727[IoP STACKS].
  2. G. Ahlers, Phys. Rev. Lett. 33 (1974), 1185[APS].
  3. J. P. Gollub and H. L. Swinney, Phys. Rev. Lett. 35 (1975), 927[APS].
  4. H. B. Møller and T. Riste, Phys. Rev. Lett. 34 (1975), 996[APS].
  5. S. Kai, M. Araoka, H. Yamazaki and K. Hirakawa, J. Phys. Soc. Jpn. 40 (1976), 305[JPSJ].
  6. K. Matsuno, Phys. Lett. A 31 (1970), 335[CrossRef].
  7. S. Kabashima, H. Yamazaki and T. Kawakubo, J. Phys. Soc. Jpn. 40 (1976), 921[JPSJ].
  8. A. R. Moore, J. Appl. Phys. 38 (1967), 2327[CrossRef].
  9. P. A. Gielen and R. J. J. Zijlstra, Solid State Commun. 18 (1976), 1009[CrossRef].
  10. T. L. Paoli, IEEE J. Quantum Electron. QE 11 (1975), 276[CrossRef].
  11. E. N. Lorenz, J. Atmos. Sci. 20 (1963), 130.
  12. Ja. G. Sinai, Russ. Math. Surv. 25 (1970), 137.
  13. J. Ford, Adv. Chem. Phys. 24 (1973), 155; in Fundamental Problems in Statistical Mechanics, III, edited by E. G. D. Cohen (North-Holland Amsterdam, 1975).
  14. B. V. Chirikov, F. M. Izrailev and V. A. Tayursky, Comput. Phys. Commun. 5 (1973), 11[CrossRef].
  15. D. Ruelle and F. Takens, Commun. Math. Phys. 20 (1971), 167[CrossRef].
  16. J. B. McLaughlin and P. Martin, Phys. Rev. A 12 (1975), 186[APS].
  17. O. E. Rössler, Z. Naturforsch. a 31 (1976), 259.
  18. O. E. Rössler, Phys. Lett. A 57 (1976), 397[CrossRef].
  19. K. Nakamura, J. Phys. Soc. Jpn. 38 (1975), 46[JPSJ].
  20. R. M. May, Nature 256 (1975), 165[CrossRef]; J. Theor. Biol. 51 (1975), 511.
  21. K. Matsuno, Phys. Rev. A 11 (1975), 1016[APS].
  22. M. Suzuki, Prog. Theor. Phys. 56 (1976), 77[PTP]; ibid. 56 (1976), 477[PTP].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 62 (1993) pp. 3639-3650 :
    Chaotic Current Oscillations in the Gunn-Effect Device Under the dc and the rf Bias Voltages
    Ken-ichi Oshio and Hideo Yahata
  2. Journal of the Physical Society of Japan 67 (1998) pp. 1050-1055 :
    Pattern Transition and Chaos in Nonlinear Semiconductors
    Yuo-Hsien Shiau, Yi-Chen Cheng and Chin-Kun Hu
  3. Progress of Theoretical Physics Vol. 59 No. 1 (1978) pp. 64-75 :
    Numerical Experiments on Trajectory Instabilities in Dissipative Systems
    Ki-ichi Nakamura
  4. Progress of Theoretical Physics Supplement No.64 (1978) pp. 378-388 :
    Trajectory Instabilities and Stochastic Behavior in Dissipative Systems with Multiple Steady States
    Ki-ichi Nakamura

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