Nonlinear Dynamics of a Metabolic Process of the Atherosclerosis

Abstract

A mathematical model of the metabolic process of atherosclerosis is constructed. The functioning of the polyenzymatic prostacyclin-thromboxane system of blood and the influence of a level of “bad cholesterol", namely low density lipoproteins (LDL), on it are studied. With the help of the numerical experiment, we analyze the influence of the concentration of molecules of fat on hemostasis of blood vessels. The kinetic curves for components of the system, phase-periodic bifurcation diagrams, attractors for various modes, and Poincare cross-section and image of a strange attractor are constructed. The complete spectra of Lyapunov’s exponents, divergencies, KS-entropies, predictability horizons, and Lyapunov dimensions of the fractality of strange attractors are calculated. Conclusions about the structural-functional connections, which determine the dependence of hemostasis of a circulatory system on the level of cholesterol in blood are drawn.