Classification of global phase portraits of a system of Liénard type
type: Item
instance of: scholarly article
title: Classification of global phase portraits of a system of Liénard type
zbMATH Open document ID: 0840.34020
author: Jitsuro Sugie
author: T. Hara
published in: Journal of Mathematical Analysis and Applications
publication date: 1995-11-01T00:00:00Z
review text: This paper concerns a classification of global phase portraits generated by a Liénard differential equation, the two functions of which satisfy conditions called ``deformed mirror symmetry'' for the phase trajectories. These conditions lead to non-dissipative trajectories, for which the authors define separatrices limiting regions of the phase plane, where the qualitative behavior of solutions remain the same. The different classes identified are illustrated by examples with continuous but piecewise differentiable data. References do not quote publications from the former Soviet Union, where the research groups have been very active in the nonlinear dynamics field since 1935.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 811586
zbMATH Keywords: periodic solutions
zbMATH Keywords: conservative systems
zbMATH Keywords: deformed mirror symmetry
zbMATH Keywords: global phase portraits
zbMATH Keywords: Liénard differential equation
zbMATH Keywords: separatrices
reviewed by: Christian Mira
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1234
OpenAlex ID: W2060892459
DOI: 10.1006/JMAA.1995.1234
description: scientific article; zbMATH DE number 811586