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Temporal properties of some biological systems and their fractal attractors

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Abstract

In this paper we analyse time series data as the growth of organisms using markers such as treerings and otolith deposits (fish). The series studied belong to two tree species (Pinus uncinata, Fagus sylvatica) and one fish species (Dicentrarchus labrax). Spectral analyses of the time series growth show that the main frequencies of fluctuation may be due to variations of the energy input. However, any causal explanation must consider the internal continuous readjustment in the system as reported by the corresponding chaotic properties of the asymptotic decay of the spectra time structure. Since the output of noisy and chaotic systems tend to show similar spectral densities, an attempt to differentiate them has been carried out. The chaotic behaviour has been characterized by the study of the attractors. The dimmensions of these multiple topologies were 3.2 and 3.4 for the tree species and 2.3 for the fish species. Therefore, we are dealing with fractal attractors and the minimum number of variables that can be used to describe the systems are 4 and 3 respectively. It is suggested that some of the variables that most influence growth are those obtained by the response functions in the case of trees.

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Authors and Affiliations

  1. University of Barcelona, Avgda Diagonal, 645, 08028, Barcelona, Spain

    Emilia Gutierrez

  2. Dept of Psychiatry and Clinical Psychobiology, University of Barcelona, Adolf Florensa s/n, 08028, Barcelona, Spain

    Helena Almirall

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  1. Emilia Gutierrez
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  2. Helena Almirall
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Gutierrez, E., Almirall, H. Temporal properties of some biological systems and their fractal attractors. Bltn Mathcal Biology 51, 785–800 (1989). https://doi.org/10.1007/BF02459660

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  • DOI: https://doi.org/10.1007/BF02459660

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