ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Podlazov A. V. Competitors’ probability distribution law, state scale invariance and linear growth models. Izvestiya VUZ. Applied Nonlinear Dynamics, 2002, vol. 10, iss. 1, pp. 20-43. DOI: 10.18500/0869-6632-2002-10-1-20-43

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Language: 
Russian
Heading: 
Review of Actual Problems of Nonlinear Dynamics
Article type: 
Article
DOI: 
10.18500/0869-6632-2002-10-1-20-43

Competitors’ probability distribution law, state scale invariance and linear growth models

Autors: 
Podlazov Andrej Viktorovich, Keldysh Institute of Applied Mathematics (Russian Academy of Sciences)
Abstract: 

The scale invariance is one of the distinguishers of the holistic behavior. Self-organized critical systems and systems with coherent noise giving examples of the scale invariance consist of essentially nonlinear elements. On the contrary, linear growth models with scale invariant properties are formulated in the paper.

Since the wholeness can’t arise from linear schemes, it is initially included in thе rules of the proposed models by means of using the information about the cumulative characteristics оf the system. The presence of such «seed оf the holistic properties» is quite enough for the distribution of system parts sizes to be power-law.

Besides that the questions of statistical samples processing for the construction of rank dependences, the analysis of the role of their parameters and the qualitative properties of systems described by power law probability distributions are considered in the paper.

Key words: 
-
Acknowledgments: 
This work was supported by RFBR (project No. 01-01-00628) and RGNF (project No. 99-03-19696).
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Received: 
13.12.2001
Accepted: 
25.01.2002
Available online: 
13.12.2023
Published: 
31.07.2002
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