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ISSN 2071-0194   Ukr. J. Phys. 2015, Vol. 60, N 6, p.561-574
doi:10.15407/ujpe60.06.0561   Paper

Grytsay V.I.

Bogolyubov Institute for Theoretical Physics, Nat. Acad. of Sci. of Ukraine
(14b, Metrolohichna Str., Kyiv 03680, Ukraine; e-mail: vgrytsay@bitp.kiev.ua)

Lyapunov Indices and the Poincaré Mapping in a Study of the Stability of the Krebs Cycle

Section: Nonlinear processes
Language: English

Abstract: On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxylic acid cycle). For the first time, we consider its consistency and stability, which depend on the dissipation of a transmembrane potential formed by the respiratory chain in the plasmatic membrane of a cell. The phaseparametric characteristic of the dynamics of the ATP level depending on a given parameter is constructed. The scenario of formation of multiple autoperiodic and chaotic modes is presented. Poincar´e sections and mappings are constructed. The stability of modes and the fractality of the obtained bifurcations are studied. The full spectra of Lyapunov indices, divergences, KS-entropies, horizons of predictability, and Lyapunov dimensionalities of strange attractors are calculated. Some conclusions about the structural-functional connections determining the dependence of the cell respiration cyclicity on the synchronization of the functioning of the tricarboxylic acid cycle and the electron transport chain are presented.

Key words: Krebs cycle, metabolic process, self-organization, strange attractor, bifurcation, Feigenbaum scenario.