IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v323y2003icp263-293.html
   My bibliography  Save this article

Self-organized criticality within fractional Lorenz scheme

Author

Listed:
  • Olemskoi, Alexander I.
  • Khomenko, Alexei V.
  • Kharchenko, Dmitrii O.

Abstract

The theory of a flux steady-state related to avalanche formation is presented for the simplest model of a sand pile within the framework of the Lorenz approach. The stationary values of sand velocity and sand pile slope are derived as functions of a control parameter (driven sand pile slope). The additive noise of above values are introduced for building a phase diagram, where the noise intensities determine both avalanche and non-avalanche domains, as well as mixed one. Corresponding to the SOC regime, the last domain is crucial to affect of the noise intensity of the vertical component of sand velocity and especially sand pile slope. To address to a self-similar behavior, a fractional feedback is used as an efficient ingredient of the modified Lorenz system. In the spirit of Edwards paradigm, an effective thermodynamics is introduced to determine a distribution over an avalanche ensemble with negative temperature. Steady-state behavior of the moving grains number, as well as non-extensive values of entropy and energy is studied in detail. The power law distribution over the avalanche size is described within a fractional Lorenz scheme, where the energy noise plays a crucial role. This distribution is shown to be a solution of both fractional and nonlinear Fokker–Planck equation. As a result, we obtain new relations between the exponent of the size distribution, fractal dimension of phase space, characteristic exponent of multiplicative noise, number of governing equations, dynamical exponents and non-extensivity parameter.

Suggested Citation

  • Olemskoi, Alexander I. & Khomenko, Alexei V. & Kharchenko, Dmitrii O., 2003. "Self-organized criticality within fractional Lorenz scheme," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 323(C), pages 263-293.
    • Handle: RePEc:eee:phsmap:v:323:y:2003:i:c:p:263-293
    DOI: 10.1016/S0378-4371(02)01991-X
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843710201991X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(02)01991-X?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrey Dmitriev & Vasily Kornilov & Svetlana Maltseva, 2018. "Complexity of a Microblogging Social Network in the Framework of Modern Nonlinear Science," Complexity, Hindawi, vol. 2018, pages 1-11, December.
    2. Belokolos, E.D. & Kharchenko, V.O. & Kharchenko, D.O., 2009. "Chaos in a generalized Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2595-2605.
    3. Andrey Dmitriev & Victor Dmitriev & Stepan Balybin, 2019. "Self-Organized Criticality on Twitter: Phenomenological Theory and Empirical Investigation Based on Data Analysis Results," Complexity, Hindawi, vol. 2019, pages 1-16, December.

    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:phsmap:v:323:y:2003:i:c:p:263-293. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.