Email this article The ultrametrical dynamics for the closed fractal-cluster resource models
- Authors: Volov V.T.1, Zubarev A.P.1
-
Affiliations:
- Samara State Transport University
- Issue: Vol 17, No 1 (2013)
- Pages: 343-351
- Section: Articles
- URL: https://journals.rcsi.science/1991-8615/article/view/34722
- DOI: https://doi.org/10.14498/vsgtu1152
- ID: 34722
Cite item
Full Text
Abstract
The evolution scenario of the resource distribution in the fractal-cluster systems which are identified as organism on Burdakov's classification is suggested. In this model the resource distribution dynamics is determined by the ultrametric structure of the fractal-cluster space. Thus for each cluster there is the characteristic time of its transition to an equilibrium state defined by ultrametric size of the cluster. The general equation that describes that dynamics is presented. The numeric solution for that equation for the certain types of resource transformation between clusters is received. The problem of identification of parameters of model with reference to real systems is discussed.
Full Text
##article.viewOnOriginalSite##About the authors
Vyacheslav Teodorovich Volov
Samara State Transport University
Email: volovvt@mail.ru
Candidate of physico-mathematical sciences, Professor
Alexander Petrovich Zubarev
Samara State Transport University
Email: apzubarev@mail.ru
Candidate of physico-mathematical sciences, Associate professor
References
- R. Rammal, G. Toulouse, M. A. Virasoro, "Ultrametricity for physicists", Rev. Modern Phys., 58:3 (1986), 765-788
- B. Dragovich, A. Yu. Khrennikov, S. V. Kozyrev, I. V. Volovich, "On -adic mathematical physics", p-Adic Numb. Ultr. Anal. Appl., 1:1 (2009), 1-17
- V. Dotsenko, An Introduction to the Spin Glasses and Neural Networks, World Scientific Lecture Notes in Physics, 54, World Scientific, Singapure, 1994, 156 pp.
- A. T. Ogielski, D. L. Stein, "Dynamics on Ultrametric Spaces", Phys. Rev. Lett., 55:15 (1985), 1634–1637
- V. A. Avetisov, A. H. Bikulov, S. V. Kozyrev, V. A. Osipov, "-Adic models of ultrametric diffusion constrained by hierarchical energy landscapes", J. Phys. A, Math. Gen., 35:2 (2002), 177-189
- V. A. Avetisov, A. Kh. Bikulov, V. A. Osipov, "-Adic description of characteristic relaxation in complex systems", J. Phys. A, Math. Gen., 36:15 (2003), 4239-4246
- D. Sornette, A. Johansen, "A hierarchical model of financial crashes", Phys. A, 261:3-4 (1998), 581-598
- R. N. Mantenga, H. E. Stanley, An introduction to econophysics. Correlations and complexity in finance, Cambridge Univ. Press, Cambridge, 2000, x+148 pp.
- А. Х. Бикулов, А. П. Зубарев, Л. В. Кайдалова, "Иерархическая динамическая модель финансового рынка вблизи точки обвала и -адический математический анализ", Вестн. Сам. гос. техн. ун-та. Сер. Физ.-мат. науки, 2006, № 42, 135-140
- W. H. Schikhof, Ultrametric calculus. An introduction to -adic analysis, Cambridge Studies in Advanced Mathematics, 4, Cambridge Univ. Press, Cambridge, 1984, viii+306 pp.
- B. C. Владимиров, И. В. Волович, Е. И. Зеленов, -Aдический анализ и математическая физика, Физматлит, М., 1994, 352 с.
- В. М. Шелкович, А. Ю. Хренников, Современный -адический анализ и математическая физика. Теория и приложения, Физматлит, М., 2012, 452 с.
- M. V. Dolgopolov, A. P. Zubarev, "Some Aspects of -Adic Analysis and Its Applications to -Adic Stochastic Processes", p-Adic Numb. Ultr. Anal. Appl., 1:3 (2011), 39–51
- В. Т. Волов, Экономика, флуктуации и термодинамика, СНЦ РАН, Самара, 2001, 222 с.
- В. Т. Волов, Фрактально-кластерная теория управления образовательными структурами, Казанск. гос. ун-т, Казань, 2000, 387 с.
- C. W. Gardiner, Handbook of stochastic methods. For physics, chemistry and the natural sciences. Second edition, Springer Series in Synergetics, 13, Springer Verlag, Berlin, 1985, xx+442 pp.
Supplementary files
