Phase portraits of continuous piecewise linear Liénard differential systems with three zones

Shimin Li; Jaume Llibre

doi:10.1016/j.chaos.2018.12.037

Phase portraits of continuous piecewise linear Liénard differential systems with three zones

Shimin Li, Jaume Llibre

Department of Mathematics

Research output: Contribution to journal › Article › Research

2 Citations (Scopus)

Abstract

© 2019 Elsevier Ltd Phase portraits are an invaluable tool in studying differential systems. Most of known results about global phase portraits are related to the smooth differential systems. This paper deals with a class of planar continuous piecewise linear Liénard differential systems with three zones separated by two vertical lines without symmetry. We provide the topological classification of the phase portraits in the Poincaré disc for systems having a unique singular point located in the middle zone.

Original language	English
Pages (from-to)	149-157
Journal	Chaos, Solitons and Fractals
Volume	120
DOIs	https://doi.org/10.1016/j.chaos.2018.12.037
Publication status	Published - 1 Mar 2019

Keywords

Limit cycle
Liénard system
Phase portrait
Piecewise linear differential system

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title = "Phase portraits of continuous piecewise linear Li{\'e}nard differential systems with three zones",

abstract = "{\textcopyright} 2019 Elsevier Ltd Phase portraits are an invaluable tool in studying differential systems. Most of known results about global phase portraits are related to the smooth differential systems. This paper deals with a class of planar continuous piecewise linear Li{\'e}nard differential systems with three zones separated by two vertical lines without symmetry. We provide the topological classification of the phase portraits in the Poincar{\'e} disc for systems having a unique singular point located in the middle zone.",

keywords = "Limit cycle, Li{\'e}nard system, Phase portrait, Piecewise linear differential system",

author = "Shimin Li and Jaume Llibre",

year = "2019",

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language = "English",

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journal = "Chaos, Solitons and Fractals",

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AU - Li, Shimin

AU - Llibre, Jaume

PY - 2019/3/1

Y1 - 2019/3/1

N2 - © 2019 Elsevier Ltd Phase portraits are an invaluable tool in studying differential systems. Most of known results about global phase portraits are related to the smooth differential systems. This paper deals with a class of planar continuous piecewise linear Liénard differential systems with three zones separated by two vertical lines without symmetry. We provide the topological classification of the phase portraits in the Poincaré disc for systems having a unique singular point located in the middle zone.

AB - © 2019 Elsevier Ltd Phase portraits are an invaluable tool in studying differential systems. Most of known results about global phase portraits are related to the smooth differential systems. This paper deals with a class of planar continuous piecewise linear Liénard differential systems with three zones separated by two vertical lines without symmetry. We provide the topological classification of the phase portraits in the Poincaré disc for systems having a unique singular point located in the middle zone.

KW - Limit cycle

KW - Liénard system

KW - Phase portrait

KW - Piecewise linear differential system

U2 - 10.1016/j.chaos.2018.12.037

DO - 10.1016/j.chaos.2018.12.037

M3 - Article

VL - 120

SP - 149

EP - 157

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

SN - 0960-0779

ER -