MATRIX PROCESS MODELLING: ON ONE CLASS OF INFINITE-ORDER SYSTEMS OF DIFFERENTIAL EQUATIONS AND ON DELAY DIFFERENTIAL EQUATIONS

SUMMARY Motivation: In recent years, intensive study of gene networks, genetically controlled metabolic paths, signal transduction paths, and other complex genetic-molecular systems has been started. Presently, these studies are reaching a qualitatively new level due to wide use of microarray analysis, which makes it possible to reveal functions of many hundreds and even thousands of genes in a single experiment. Analysis of huge amounts of experimental data, which reflect complex processes in genetic-molecular systems, is impossible without efficient mathematical methods. Results: In the present paper we consider a class of models describing matrix branching processes with an unrestrictedly increasing number of stages. We show that the last components of solutions of corresponding systems of ordinary differential equations tend to a solution of one delay differential equation.