Localization of the attractors of the non-autonomous Liénard equation by the method of discontinuous comparison systems
type: Item
instance of: scholarly article
title: Localization of the attractors of the non-autonomous Liénard equation by the method of discontinuous comparison systems
zbMATH Open document ID: 0880.34055
DOI: 10.1016/0021-8928(96)00042-1
published in: Journal of Applied Mathematics and Mechanics
publication date: 1998-02-12T00:00:00Z
review text: Consider the non-autonomous Liénard equation \[ dy/dt=-\mu(F(y)- E(t))- x,\quad dx/dt=y,\tag{\(*\)} \] where \(F\) and \(E\) are Lipschitzian, \(\mu\) is a positive parameter. By means of discontinuous comparison systems of dry friction type, the author constructs a simply connected region containing the global attractor of \((*)\), provided the right-hand side of \((*)\) satisfies certain conditions, which are quite common for Liénard systems. As an application, an autonomous system of van der Pol's type is considered.
Mathematics Subject Classification ID: 34D45
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 1042192
zbMATH Keywords: non-autonomous
zbMATH Keywords: Liénard equation
zbMATH Keywords: discontinuous comparison systems
zbMATH Keywords: global attractor
author: G. A. Leonov
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
full work available at URL: 0021-8928(96)00042-1
OpenAlex ID: W2056791597
cites work: Q5731955
cites work: Q5345170
cites work: Q4693183
cites work: Q5752850
cites work: On non-linear differential equations of the second order. II. The equation \(\ddot y+kf(y)\dot y+g(y,k)=p(t)=p_1(t)+kp_2(t)\); \(k>0,f(y)\geq 1\)
cites work: Oscillations in systems with non-linear damping
description: scientific article; zbMATH DE number 1042192