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Evolution of the Dynamic Dissipative Systems as a Temporal “Colour” Fractal

In: Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media

Author

Listed:
  • Serge F. Timashev

    (Karpov Institute of Physical Chemistry)

  • Yegor Yu. Budnikov

    (Karpov Institute of Physical Chemistry)

  • Vladimir L. Klochikhin

    (Karpov Institute of Physical Chemistry)

  • Irina G. Kostuchenko

    (Karpov Institute of Physical Chemistry)

  • Sergey G. Lakeev

    (Karpov Institute of Physical Chemistry)

  • Alexander V. Maximychev

    (Karpov Institute of Physical Chemistry)

Abstract

New possibilities in elaborating the evolution of dynamical dissipative system evolution are associated with the ideas of nonlinear system dynamics and deterministic chaos1–4. In this paper a new phenomenological method for analysis of non-linear dissipative system dynamics, which may be called flicker-noise spectroscopy5–8, is presented. An algorithm is developed which allows us to obtain as many phenomenological parameters — “passport data” — as necessary for the description and characterization of the dynamic system’s state and the changes of its state during evolution. We demonstrate the application of this approach for analysis of the time series by describing various phenomena. Spatial space structures may be examined in a similar manner.

Suggested Citation

  • Serge F. Timashev & Yegor Yu. Budnikov & Vladimir L. Klochikhin & Irina G. Kostuchenko & Sergey G. Lakeev & Alexander V. Maximychev, 1999. "Evolution of the Dynamic Dissipative Systems as a Temporal “Colour” Fractal," Springer Books, in: Ludmila A. Uvarova & Arkadii E. Arinstein & Anatolii V. Latyshev (ed.), Mathematical Models of Non-Linear Excitations, Transfer, Dynamics, and Control in Condensed Systems and Other Media, pages 17-50, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4615-4799-0_2
    DOI: 10.1007/978-1-4615-4799-0_2
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