Application of M-Matrices for the Study of Mathematical Models of Living Systems

Abstract

Some results are presented of application of M-matrices to the study the stability problem of the equilibriums of differential equations used in models of living systems. The models studied are described by differential equations with several delays, including distributed delay, and by high-dimensional systems of differential equations. To study the stability of the equilibriums the linearization method is used. Emerging systems of linear differential equations have a specific structure of the right-hand parts, which allows to effectively use the properties of M-matrices. As examples, the results of studies of models arising in immunology, epidemiology and ecology are presented.

Matrix stability and instability criteria for some systems of linear delay differential equations

“…Присутствие в системе (1) диагональной матрицы B, как правило, связано с учетом процессов естественной гибели, превращений или миграционных потоков элементов моделируемых живых систем. Примеры таких моделей приведены в работах [1], [2], [3], [4].…”