Uniqueness and Non-uniqueness of Limit Cycles for Piecewise Linear Differential Systems with Three Zones and No Symmetry

Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems with two and three zones and no symmetry. For planar systems with three linearity zones, the existence of two limit cycles surroun...

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Detalles Bibliográficos
Autores: Llibre, Jaume|||0000-0002-9511-5999, Ponce, Enrique|||0000-0003-0467-5032, Valls, Clàudia|||0000-0001-8279-1229
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:145353
Acceso en línea:https://ddd.uab.cat/record/145353
https://dx.doi.org/urn:doi:10.1007/s00332-015-9244-y
Access Level:acceso abierto
Palabra clave:Liénard piecewise linear differential systems
Limit cycles
Nonlinear control systems
Periodic orbit
Descripción
Sumario:Some techniques for proving the existence and uniqueness of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems with two and three zones and no symmetry. For planar systems with three linearity zones, the existence of two limit cycles surrounding the only equilibrium point at the origin is rigorously shown for the first time. The usefulness of the achieved analytical results is illustrated by considering non-symmetric memristor-based electronic oscillators.