MATHEMATICAL ANALYSIS OF QUALITATIVE CHARACTERISTICS OF SOLUTIONS OF SYSTEMS OF DIFFERENTIAL EQUATIONS DESCRIBING BIOCHEMICAL PROCESSES RATES

Abstract

The article considers mathematical modeling of biochemical processes rates in biological systems. It is given the
system of differential equations which, in the general case, describes biochemical processes rates. It is noticed in which cases
the system of differential equations can be solved analytically and when the exact solution can be obtained. It is shown the
importance of qualitative characteristics to predict changes in the nature of the system behavior when conditions change. It is
analyzed how the state of the system is represented at an arbitrary moment of time. It is shown that qualitative analysis makes
it possible to determine the nature the solution of the system of differential equations by the form of phase trajectories. It is
shown how the change in the state of the system over time is described by the evolution operator. Mathematical analysis of
qualitative characteristics of solutions of systems of differential equations describing biochemical processes rates is performed
in the article. Examples of phase portraits are considered and investigated.