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FIZIKA A 10 (2001) 3 , 95-104
 
ENERGY DEPENDENCE OF SELFSIMILARITY TRUNCATION IN A SYSTEM OF WEAKLY
COUPLED DISSIPATIVE OSCILLATORS RELEVANT FOR BIOLOGICAL SYSTEMS
VLADIMIR PAARa, NENAD PAVINa and MARIJA ROSANDIĆb
aDepartment of Physics, Faculty of Science, University of
Zagreb, Zagreb, Croatia
bUniversity Hospital Rebro, Department of Internal Medicine,
University of Zagreb, Zagreb, Croatia
Dedicated to Professor Kseno Ilakovac on the occasion of his 70th
birthday
Received 28 June 2001; Accepted 17 December 2001
Online 30 December 2001
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.
PACS numbers: 05.45.Pq, 87.80.+y
UDC 53.047
Keywords: fractals, truncated fractals, basin boundaries, coupled oscillators,
biological oscillators, biological systems, obstruction to estimating long term behaviour,
control of biological processes
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