The Onset and the Development of Chaotic Structures in Dissipative Media

  • A. V. Gaponov-Grekhov
  • M. I. Rabinovich
  • I. M. Starobinets
Conference paper
Part of the Springer Series in Synergetics book series (SSSYN, volume 28)


The appearance of space structures in dissipative media results from the development of space-inhomogeneous instabilities and their subsequent stabilization due to the balance between the internal dissipative loss in the medium and the pumping from the source of nonequilibrium. This balance, in the average, may take place both the regular, completely ordered states and in nonstationary chaotic structures.


Couette Flow Strange Attractor Regular Structure Taylor Vortex Single 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    M. Eigen and P. Schuster. The Hypercycle. A Principle of Natural Self-Organization, Springer (1979)Google Scholar
  2. 2.
    A.V. Gaponov-Grekhov and M.I. Rabinovich. Nonstationary Structures - Chaos and Order. In: Synergetics of Brain, ed. H. Haken, Springer (1983)Google Scholar
  3. 3.
    Yu.S. Iliashenko. - Advances in Mechanics (1982) v. 5, No 1-2, p. 31 - 64Google Scholar
  4. 4.
    C. Foias and R. Temam. - J. Math. Pures et Appl. (1979), 58; 3Google Scholar
  5. 5.
    A.V. Babin and M.I. Vishik. - Uspekhi Mat. Nauk, (1983), v.38, No 4 (232), p.133-187Google Scholar
  6. 6.
    Y. Kuramoto. Induced Chemical Turbulence. In: Dynamics of Synergetic Systems, ed. H.Haken, Springer (1980) p. 134 - 146CrossRefGoogle Scholar
  7. 7.
    P. Berge and M. Dubois. - Phys. Lett. (1983) V.93A, No 8, p.365- 368Google Scholar
  8. 8.
    N. Kopell and L.N. Howard. - Studies in Appl. Math. (1973), v. 52. p. 291 - 328MathSciNetMATHGoogle Scholar
  9. 9.
    V.S. L’vov and A.A. Predtechensky. Step by Step Transition to Turbulence in the Couette Flow. In: Nonlinear Waves. Stochasticity and Turbulencef Gorky, Inst, of Appl. Phys. Acad. Sci. USSR (1980) p. 57Google Scholar
  10. 10.
    I. Shimada and T. Nagashima. - Progr. Theor. Phys. (1979) v. 61, No 6, p. 1605 - 1616ADSMATHCrossRefGoogle Scholar
  11. 11.
    V.I. Arnold and A. Avez. Ergodic Problems of Classical Mechanics, Benjamin, New York (1968)Google Scholar
  12. 12.
    Y. Pomeau and P. Manneville. - Commun. Math. Phys. (1980) v. 77, p. 189ADSGoogle Scholar
  13. 13.
    F. Lidrappier. Commun. Math. Phys. (1981) v. 81, p. 229ADSCrossRefGoogle Scholar
  14. 14.
    J.P. Eckmann. Rev. Modern. Phys. (1981) v. 53, p. 643.MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • A. V. Gaponov-Grekhov
    • 1
  • M. I. Rabinovich
    • 1
  • I. M. Starobinets
    • 1
  1. 1.Institute of Applied PhysicsAcademy of Sciences of the USSRSU-GorkyUSSR

Personalised recommendations