Simulation of Delay Using a System of Ordinary Differential Equations

I. S. Kashchenko, S. A. Kaschenko

P.G. Demidov Yaroslavl State University

Abstract: A class of systems of ordinary differential equations simulating the delay effect is investigated. Systems of ordinary differential equations whose solution properties are close to the properties of an equation with delay are proposed. Some critical cases in the problem of stability of an equilibrium are identified. Based on bifurcation analysis, we formulate conclusions that the behavior of solutions of the considered system of equations approaches the behavior of solutions of an equation with delay with an increase in the dimension of the system under study. Changes in the dynamical properties depending on the number of equations in the proposed system are studied.

Keywords: delay, stability, normal form.

UDC: 517.9

MSC: 37L10

Received: 12.09.2024
Revised: 20.02.2025

DOI: 10.4213/mzm14503

 English version: Mathematical Notes, 2025, 118:2, 294–308

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