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JOURNALS // Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences // Archive

Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2013 Issue 1(30), Pages 343–351 (Mi vsgtu1152)

Procedings of the 3nd International Conference "Mathematical Physics and its Applications"
Complex Systems, Quantum Mechanics, Information Theory

The ultrametrical dynamics for the closed fractal-cluster resource models

V. T. Volov, A. P. Zubarev

Samara State Transport University, Samara, 443066, Russia

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.

Keywords: hierarchical structures, ultrametric, fractal-cluster models, mathematical modeling, socio-economic systems, resource allocation.

UDC: 519.866:303.72

MSC: Primary 82C44; Secondary 93A30, 11Z05, 82D30

Original article submitted 05/XI/2012
revision submitted – 07/I/2013

DOI: 10.14498/vsgtu1152



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