Lyapunov Indices and the Poincare Mapping in a Study of the Stability of the Krebs Cycle
DOI:
https://doi.org/10.15407/ujpe60.06.0561Keywords:
Krebs cycle, metabolic process, self-organization, strange attractor, bifurcation, Feigenbaum scenarioAbstract
On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxylic acid cycle). For the rst 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 phase-parametric 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. Poincare 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.
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