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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Bibliographic Details
Authors: Llibre, Jaume|||0000-0002-9511-5999, Ponce, Enrique|||0000-0003-0467-5032, Valls, Clàudia|||0000-0001-8279-1229
Format: article
Publication Date:2015
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:145353
Online Access:https://ddd.uab.cat/record/145353
https://dx.doi.org/urn:doi:10.1007/s00332-015-9244-y
Access Level:Open access
Keyword:Liénard piecewise linear differential systems
Limit cycles
Nonlinear control systems
Periodic orbit
Description
Summary: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.