IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v34y2007i1p51-61.html
   My bibliography  Save this article

The stochastic nature of complexity evolution in the fractional systems

Author

Listed:
  • Stanislavsky, Aleksander A.

Abstract

The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in the temporal behavior of such systems. This model provides a rigorous justification of the energy criterion introduced by Jonscher. The meaning of the parameters into the empirical response functions is clarified. This treatment sheds a fresh light on the nature of not only the dielectric relaxation but also mechanical, luminescent and radiochemical ones. In the case of the Cole–Cole response there exists a direct link between the notation of the fractional derivative (appearing in the fractional macroscopic equation often proposed) and the model. But the macroscopic response equations, relating to the Cole–Davidson and Havriliak–Negami relaxations, have a more general integro-differential form in comparison with the ordinary fractional one.

Suggested Citation

  • Stanislavsky, Aleksander A., 2007. "The stochastic nature of complexity evolution in the fractional systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(1), pages 51-61.
  • Handle: RePEc:eee:chsofr:v:34:y:2007:i:1:p:51-61
    DOI: 10.1016/j.chaos.2007.01.049
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907000896
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2007.01.049?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:34:y:2007:i:1:p:51-61. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.