Limit cycles for planar piecewise linear differential systems via first integrals

Jaume Llibre; Eduardo Nuñez; Antonio E. Teruel

doi:https://doi.org/10.1007/BF02969332

Limit cycles for planar piecewise linear differential systems via first integrals

Jaume Llibre, Eduardo Nuñez, Antonio E. Teruel

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

12 Citations (Scopus)

Abstract

Using first integrals we introduce an alternative tool to the Poincaré maps in order to study the limit cycles of piecewise linear differential systems. It is also shown that an usual relaxation oscillation phenomenon occurrs in a two-parameter family of planar piecewise linear vector fields.

Original language	English
Pages (from-to)	29-50
Journal	Qualitative Theory of Dynamical Systems
Volume	3
DOIs	https://doi.org/10.1007/BF02969332
Publication status	Published - 1 Dec 2002

Keywords

First integrals
Limit cycles
Piecisewise linear differential systems

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title = "Limit cycles for planar piecewise linear differential systems via first integrals",

abstract = "Using first integrals we introduce an alternative tool to the Poincar{\'e} maps in order to study the limit cycles of piecewise linear differential systems. It is also shown that an usual relaxation oscillation phenomenon occurrs in a two-parameter family of planar piecewise linear vector fields.",

keywords = "First integrals, Limit cycles, Piecisewise linear differential systems",

author = "Jaume Llibre and Eduardo Nu{\~n}ez and Teruel, {Antonio E.}",

year = "2002",

month = dec,

day = "1",

doi = "https://doi.org/10.1007/BF02969332",

language = "English",

volume = "3",

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journal = "Qualitative Theory of Dynamical Systems",

issn = "1575-5460",

publisher = "Springer Science + Business Media",

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T1 - Limit cycles for planar piecewise linear differential systems via first integrals

AU - Llibre, Jaume

AU - Nuñez, Eduardo

AU - Teruel, Antonio E.

PY - 2002/12/1

Y1 - 2002/12/1

N2 - Using first integrals we introduce an alternative tool to the Poincaré maps in order to study the limit cycles of piecewise linear differential systems. It is also shown that an usual relaxation oscillation phenomenon occurrs in a two-parameter family of planar piecewise linear vector fields.

AB - Using first integrals we introduce an alternative tool to the Poincaré maps in order to study the limit cycles of piecewise linear differential systems. It is also shown that an usual relaxation oscillation phenomenon occurrs in a two-parameter family of planar piecewise linear vector fields.

KW - First integrals

KW - Limit cycles

KW - Piecisewise linear differential systems

U2 - https://doi.org/10.1007/BF02969332

DO - https://doi.org/10.1007/BF02969332

M3 - Article

VL - 3

SP - 29

EP - 50

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

SN - 1575-5460

ER -