Limit cycles for m-piecewise discontinuous polynomial Liénard differential equations

We provide lower bounds for the maximum number of limit cycles for the m-piecewise discontinuous polynomial differential equations x = y + sgn(gm (x, y))F (x), y = -x, where the zero set of the function sgn(gm (x, y)) with m = 2, 4, 6, . . . is the product of m/2 straight lines passing through the o...

Descripción completa

Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Teixeira, Marco Antonio|||0000-0002-5386-9282
Tipo de recurso: artículo
Fecha de publicación:2015
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:145367
Acceso en línea:https://ddd.uab.cat/record/145367
https://dx.doi.org/urn:doi:10.1007/s00033-013-0393-2
Access Level:acceso abierto
Palabra clave:Averaging theory
Liénard equation
Limit cycles
Piecewise differential equation
Descripción
Sumario:We provide lower bounds for the maximum number of limit cycles for the m-piecewise discontinuous polynomial differential equations x = y + sgn(gm (x, y))F (x), y = -x, where the zero set of the function sgn(gm (x, y)) with m = 2, 4, 6, . . . is the product of m/2 straight lines passing through the origin of coordinates dividing the plane in sectors of angle 2π/m, and sgn(z) denotes the sign function.