CORPORATE DYNAMICS OF SYSTEMS OF LOGISTIC DELAY EQUATIONS WITH LARGE DELAY CONTROL

Abstract

A system of two logistic equations with delay coupled by delayed control is considered. It is shown that in the case of a sufficiently large delay control coefficient the problem of the dynamics of the initial systems is reduced to studying the non-local dynamics of special families of partial differential equations that do not contain small and large parameters. New interesting dynamic phenomena were discovered on the basis of the results of numerical analysis. Systems of three logistic delay equations with two types of ”diffusion” relation were considered. Special families of partial differential equations that do not contain small and large parameters were also constructed for each of these systems. The results of the study of the original equations dynamic properties are presented. It is shown that the difference in the dynamics of the considered systems of three equations may be of a fundamental nature.

Keywords

• large control
• quasinormal form
• delay