Dynamics of delay systems with rapidly oscillating coefficients
type: Item
instance of: scholarly article
title: Dynamics of delay systems with rapidly oscillating coefficients
zbMATH Open document ID: 1402.34079
DOI: 10.1134/S0012266118010032
published in: Differential Equations
publication date: 2018-07-06T00:00:00Z
review text: The present paper considers the generalization of the averaging principle to delay systems and contains the following results described in the section ``conclusion'' of the paper: 1. It is shown that the averaged equation in delay systems can be rather complicated. In particular, the averaging can take the equation from the class of equations with lumped delay to the class of equations with distributed delay. 2. An algorithm is developed for studying the stability in nearly critical cases. It is shown that the phenomenon of unbounded process of alternation between stability and instability as the frequency of oscillations increases is typical of delay equations. 3. It is shown that the variations in the parameters (with zero mean) can significantly increase the stability domain. 4. It is shown that the phenomena of unbounded process of ``creation'' and ``termination'' of steady-state modes can arise in the nonlinear case.
reviewed by: Andrej V. Plotnikov
Mathematics Subject Classification ID: 34K33
zbMATH DE Number: 6899059
zbMATH Keywords: nonlinear delay system
zbMATH Keywords: averaging
zbMATH Keywords: rapidly oscillating coefficients
zbMATH Keywords: stability
author: S. A. Kashchenko
MaRDI profile type: Publication
cites work: Q3255588
cites work: Q4050970
cites work: Q5640781
cites work: Theory of functional differential equations. 2nd ed
cites work: Q5330830
cites work: Theory and applications of partial functional differential equations
cites work: Q4056924
cites work: Q1233671
cites work: Q3961135
cites work: Stability of equilibrium state in a laser with rapidly oscillating delay feedback
cites work: Q4652395
cites work: Averaging methods in nonlinear dynamical systems
cites work: Computation of the phase detector characteristic of classical PLL
cites work: The existence of periodic solutions of \(f'(x)=-\alpha f(x-1)(1+f(x))\)
cites work: Q4002771
cites work: Q3251626
cites work: Asymptotic behavior of steady-state conditions of parabolic equations with coefficients rapidly oscillating in time and with variable region of definition
cites work: Travelling wave dynamics in a nonlinear interferometer with spatial field transformer in feedback
full work available at URL: s0012266118010032
OpenAlex ID: W2799477303
description: scientific article; zbMATH DE number 6899059