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Soviet Physics Journal

, Volume 27, Issue 6, pp 522–530 | Cite as

Model description of a chain of coupled dynamic systems near order-disorder phase transitions

  • S. P. Kuznetsov
Solid State Physics
  • 14 Downloads

Abstract

A method is suggested of phenomenological description of a chain of coupled systems, demonstrating during the variation of some parameter a transition from periodic to chaotic regimes through an infinite sequence of period doubling. The method consists of using models, chains of coupled, one-dimensional mappings. It is shown that from the point of view of chain behavior, following a large number of period doublings the coupling between the systems is a combination of two fundamental types of coupling; equality of the corresponding coupling coefficients for a chain and its models is the correspondence condition between them. A specific example is considered, a chain of parametrically excited nonlinear oscillators with dissipation.

Keywords

Phase Transition Dynamic System Couple System Model Description Nonlinear Oscillator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Literature cited

  1. 1.
    Yu. I. Neimark, The Method of Point Transformations in the Theory of Nonlinear Oscillations [in Russian], Nauka, Moscow (1972).Google Scholar
  2. 2.
    M. J. Feigenbaum, J. Stat. Phys.,19, 25 (1978).Google Scholar
  3. 3.
    M. J. Feigenbaum, J. Stat. Phys.,21, 669 (1979).Google Scholar
  4. 4.
    M. J. Feigenbaum, Commun. Math. Phys.,77, 65 (1980).Google Scholar
  5. 5.
    F. M. Izrailov, M. I. Rabinovich, and A. D. Ugodnikov, Phys. Lett.,A86, 321 (1981).Google Scholar
  6. 6.
    J. Testa, J. Perez, and C. Jeffries, Phys. Rev. Lett.,48, 74 (1982).Google Scholar
  7. 7.
    Strange Attractors [Russian translation], Mir, Moscow (1981).Google Scholar
  8. 8.
    J. D. Eckman, Rev. Mod. Phys.,53, 643 (1981).Google Scholar
  9. 9.
    T. Kai, Phys. Lett.,A6, 263 (1981).Google Scholar
  10. 10.
    S. P. Kuznetsov, Izv. Vyssh. Uchebn. Zaved., Radiofizika,25, 1364 (1982).Google Scholar
  11. 11.
    L. D. Kudryavtsev, Mathematical Analysis [in Russian], Vysshaya Shkola, Moscow (1973).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • S. P. Kuznetsov
    • 1
  1. 1.Saratov State UniversityUSSR

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