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

Abstract

On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxilic 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 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. Poincaré 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 tricarboxilic acid cycle and the electron transport chain are presented.

References in corpus (2)

• Self-organization and chaos in the metabolism of a cell
• Self-oscillatory dynamics of the metabolic process in a cell

Cited by in corpus (5)

• Spectral Analysis and Invariant Measure in the Study of a Nonlinear Dynamics of the Metabolic Process in Cells
• Self-Organization and Chaos in the Metabolism of Hemostasis in a Blood Vessel
• Autooscillatory Dynamics in a Mathematical Model of the Metabolic Process in Aerobic Bacteria. Influence of the Krebs Cycle on the Self-Organization of a Biosystem
• Spectral Analysis and Invariant Measure in Studies of the Dynamics of the Hemostasis of a Blood Vessel
• Characteristics of the Invariant Measure of the Strange Attractor of the Bacteria Mathematical Model