Limit cycles for planar piecewise linear differential systems via first integrals

Antonio E. Teruel; Eduardo Nuñez; Jaume Llibre

doi:10.1007/BF02969332

Limit cycles for planar piecewise linear differential systems via first integrals

Antonio E. Teruel, Eduardo Nuñez, Jaume Llibre

Departament de Matemàtiques

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17 Cites (Scopus)

Resum

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.

Idioma original	Anglès
Pàgines (de-a)	29-50
Revista	Qualitative Theory of Dynamical Systems
Volum	3
DOIs	https://doi.org/10.1007/BF02969332
Estat de la publicació	Publicada - 1 de des. 2002

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

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

year = "2002",

month = dec,

day = "1",

doi = "10.1007/BF02969332",

language = "English",

volume = "3",

pages = "29--50",

journal = "Qualitative Theory of Dynamical Systems",

issn = "1575-5460",

publisher = "Springer International Publishing",

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TY - JOUR

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

AU - Teruel, Antonio E.

AU - Nuñez, Eduardo

AU - Llibre, Jaume

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 - Piecisewise linear differential systems

KW - Limit cycles

KW - First integrals

UR - https://dialnet.unirioja.es/servlet/articulo?codigo=670111

UR - https://www.scopus.com/pages/publications/84896693965

U2 - 10.1007/BF02969332

DO - 10.1007/BF02969332

M3 - Article

SN - 1575-5460

VL - 3

SP - 29

EP - 50

JO - Qualitative Theory of Dynamical Systems

JF - Qualitative Theory of Dynamical Systems

ER -

Limit cycles for planar piecewise linear differential systems via first integrals

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