MATHEMATICAL STUDY OF THE STABILITY OF FIXED POINTS OF SYSTEMS OF DIFFERENTIAL EQUATIONS DESCRIBING BIOCHEMICAL PROCESSES RATES

Abstract

Mathematical study of the stability of fixed points of systems of differential equations describing biochemical processes rates is performed in the article. A system of differential equations for deviations is constructed, which describes the behavior of the system near the fixed point. An analysis of the general solution of the system of differential equations describing biochemical processes rates is made. The behavior of the systems near fixed points is investigated by the method of small perturbations. The conditions of existence of the limit cycle of the system of differential equations are investigated. For the cases when the system of differential equations cannot have an analytical solution, integrated curves are constructed by qualitative research. Phase trajectories of the system of differential equations describing biochemical processes rates are constructed. The definition of the nature of the stability of fixed points is considered and investigated.