Averaging method for multifrequency systems with lag
type: Item
instance of: scholarly article
title: Averaging method for multifrequency systems with lag
zbMATH Open document ID: 0618.34062
DOI: 10.1007/BF01055966
author: V. P. Shpakovich
published in: Ukrainian Mathematical Journal
publication date: 1985-01-01T00:00:00Z
review text: The author considers the multifrequency system with delay \[ dx/dt=\epsilon X(x,x_{\Delta},\phi,\phi_{\Delta}),\quad d\phi /dt=\omega (x)+\epsilon Y(x,x_{\Delta},\phi,\phi_{\Delta}), \] where \(x\in R^ n\), \(x_{\Delta}=x(t-\Delta)\in R^ n\), \(\phi_{\Delta}=\phi (t-\Delta)\), \(\phi =(\phi_ 1,...,\phi_ m)\), X and Y are \(2\pi\)-periodic functions with respect to \(\phi\) and \(\phi_{\Delta}\). It is proved that the norm of the difference between the solution of a two-frequency system and the solution of the corresponding averaging system is of order \(\sqrt{\epsilon}\). This result is extended to multifrequency system.
Mathematics Subject Classification ID: 34K99
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 4002580
zbMATH Keywords: multifrequency system with delay
zbMATH Keywords: averaging system
MaRDI profile type: Publication
cites work: Application of the averaging method for studying a certain class of multifrequency systems with lag
description: scientific article; zbMATH DE number 4002580