Self-oscillatory dynamics of the metabolic process in a cell

• Published in: Ukrainian biochemical journal Vol. 85; no. 2; pp. 93 - 104
• Main Authors: V. I. Grytsay, I. V. Musatenko
• Format: Journal Article
• Language: English
• Published: National Academy of Sciences of Ukraine, Palladin Institute of Biochemistry 27-04-2013
• Subjects: Lyapunov exponents; mathematical model; metabolic process; Poincaré section; self-organization; strange attractor
• ISSN: 2409-4943; 2413-5003
• DOI: 10.15407/ubj85.02.093

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.