Linearly implicit Liénard systems
type: Item
instance of: scholarly article
title: Linearly implicit Liénard systems
zbMATH Open document ID: 1213.34011
author: Ricardo Riaza
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2010-11-05T00:00:00Z
review text: The presence of nonlinearities in the capacitance and the inductance in van der Pol type electrical circuits defines a linearly implicit (or quasilinear) counterpart of the classical Liénard systems. When the reactances remain positive, the existence of a unique attracting periodic solution follows, with minor modifications, as in the classical setting. Novel results are obtained when the values of reactances may vanish at certain points of the state space; these points yield singularities of the model, and the existence of an attracting periodic solution can be characterized in terms of the behavior of certain smooth solutions crossing the singular manifold through so-called I-singularities.
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 94C05
zbMATH DE Number: 5810953
zbMATH Keywords: implicit equations
zbMATH Keywords: periodic solutions
MaRDI profile type: Publication
full work available at URL: j.na.2010.08.035
OpenAlex ID: W2052659215
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DOI: 10.1016/J.NA.2010.08.035
description: scientific article; zbMATH DE number 5810953