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 {\guillemotleft}order-chaos{\guillemotright}, {\guillemotleft}chaos-order{\guillemotright} and {\guillemotleft}order-order{\guillemotright} are found. We constructed the projections of the multidimensional phase portraits of attractors, Poincar\'e sections, and Poincar\'e 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.
Highlights
The development of a general mathematical model of cell is a very complicated task
We deal with a mathematical model of the metabolism running in a cell Arthrobacter globiformis
The mathematical model of the process under flow conditions of a bioreactor is constructed in accordance with the general scheme (Fig. 1) of metabolic processes running in Arthrobacter globiformis cells under the transformation of steroids [19,20,21,22,23,24,25,26,27,28,29,30]:
Summary
The development of a general mathematical model of cell is a very complicated task. To solve it, it is necessary to study the biochemical proces ses and the types of nonlinearities characteristic of enzyme-substrate interactions causing the appearance of the self-organization in a system. As distinct from the earlier results obtained within the model under consideration, we will calculate phase-parametric characteristics of variations of the form of attractors depending on the dissipation of a kinetic membrane potential and will show the appearance of the mutual transitions between stable and chaotic oscillations.
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