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

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