V. I. Grytsay¹, I. V. Musatenko²

¹Bogolyubov Institute for Theoretical Physics,
National Academy of Sciences of Ukraine, Kyiv;
e-mail: vgrytsay@bitp.kiev.ua;
²Taras Shevchenko National University of Kyiv, Ukraine;
e-mail: ivmusatenko@gmail.com

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.