Self-oscillatory dynamics of the metabolic process in a cell

摘要

In this work, a mathematical model of self-oscillatory dynamics of themetabolism in a cell is studied. The full phase-parametric characteristics ofvariations of the form of attractors depending on the dissipation of a kineticmembrane potential are calculated. The bifurcations and the scenarios of thetransitions {\guillemotleft}order-chaos{\guillemotright},{\guillemotleft}chaos-order{\guillemotright} and{\guillemotleft}order-order{\guillemotright} are found. We constructed theprojections of the multidimensional phase portraits of attractors, Poincar\'esections, and Poincar\'e maps. The process of self-organization of regularattractors through the formation torus was investigated. The total spectra ofLyapunov exponents and the divergences characterizing a structural stability ofthe determined attractors are calculated. The results obtained demonstrate thepossibility of the application of classical tools of nonlinear dynamics to thestudy of the self-organization and the appearance of a chaos in the metabolicprocess in a cells.