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Current issue   Ukr. J. Phys. 2014, Vol. 58, N 7, p.677-686


Grytsay V.I.1, Musatenko I.V.2

1 Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14b, Metrolohichna Str., Kyiv 03680, Ukraine; e-mail: vgrytsay@bitp.kiev.ua)
2 Taras Shevchenko National University of Kyiv, Faculty of Cybernetics,
Department of Computational Mathematics
(64, Volodymyrs’ka Str., Kyiv 01033, Ukraine; e-mail: ivmusatenko@gmail.com)

The Structure of a Chaos of Strange Attractors within a Mathematical Model of the Metabolism of a Cell

Section: Nonlinear processes
Original Author's Text: English

Abstract: This work continues the study of the earlier constructed mathematical model of the metabolic process running in a cell. We will consider autooscillations arising on the level of enzymesubstrate interactions in the nutrient and respiratory chains, which leads to the selforganization in autocatalysis of the integral metabolic process in cells. The autooscillations organize themselves in the total metabolic process of cells at autocatalysis. The behavior of the phase-parametric characteristic under a high dissipation of the kinetic membrane potential is analyzed. All possible oscillatory modes of the system and the scenario of formation and destruction of regular and strange attractors are studied. The bifurcations of the transitions “order-chaos”, “chaos-order”, “chaos-chaos” and “order-order” are calculated. The total spectra of Lyapunov indices and the divergences for all types of attractors on a part of the phase-parametric characteristic under consideration are determined. For various types of strange attractors, their Lyapunov dimensions, Kolmogorov–Sinai-entropies (KS-entropies), and “predictability horizons” are calculated. Some conclusions about the structure of the chaos of strange attractors and its influence on the stability of the metabolic process in a cell are drawn.

Key words: metabolism of a cell, attractors, Lyapunov dimensions, KS-entropies, structure of the chaos.