Self-oscillatory dynamics of the metabolic process in a cell

Abstract

In this work, a mathematical model of self-oscillatory dynamics of the metabolism in a cell is studied. The full phase-parametric characteristics of variations of the form of attractors depending on the dissipation of a kinetic membrane potential are calculated. The bifurcations and the scenarios of the transitions «order-chaos», «chaos-order» and «order-order» are found. We constructed the projections of the multidimensional phase portraits of attractors, Poincaré sections, and Poincaré maps. The process of self-organization of regular attractors through the formation torus was investigated. The total spectra of Lyapunov exponents and the divergences characterizing a structural stability of the determined attractors are calculated. The results obtained demonstrate the possibility of the application of classical tools of nonlinear dynamics to the study of the self-organization and the appearance of a chaos in the metabolic process in a cells.

12 pages,7 figures

Cited by in corpus (6)

• Self-Organization and Fractality in the Metabolic Process of Glycolysis
• 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