Energy dependence of selfsimilarity truncation in a system of weakly coupled dissipative oscillators relevant for biological systems

Paar, Vladimir and Pavin, Nenad and Rosandić, Marija (2001) Energy dependence of selfsimilarity truncation in a system of weakly coupled dissipative oscillators relevant for biological systems. Fizika A, 10 (3). pp. 95-104. ISSN 1330-0008

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Abstract

Biological fractals are truncated, i.e., their selfsimilarity extends at most over a few orders of magnitude of separation. In J. Theor. Biology 212 (2001) p. 47, we have shown that the nonlinear coupled oscillators, modeling one of the basic features of biological systems, may generate truncated fractals: a truncated fractal pattern for basin boundaries appears in a simple mathematical model of two coupled nonlinear oscillators with weak dissipation. We show here that the degree of truncation decreases with increasing energy. We point out that at the level of a sufficiently fine precision technique, the truncated fractality acts as a smooth (nonfractal) structure, leading to predictability, but at a lower level of precision it is effectively fractal, limiting the predictability of the long term behaviour of biological systems. Consequently, a possible erratic nature of the system's behaviour due to truncated fractality may disappear once the experimental errors in the measurement and/or treatment of biological system reaches a certain level of precision. We point out a possible significance of this result for the biological control of processes.

Item Type: Article
Keywords: fractals, truncated fractals, basin boundaries, coupled oscillators, biological oscillators, biological systems, obstruction to estimating long term behaviour, control of biological processes
Date: 2001
Subjects: NATURAL SCIENCES > Physics
Divisions: Faculty of Science > Department of Physics
Publisher: Hrvatsko fizikalno društvo
Depositing User: Gordana Stubičan Ladešić
Date Deposited: 15 Apr 2014 15:54
Last Modified: 15 Apr 2014 15:54
URI: http://digre.pmf.unizg.hr/id/eprint/837

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