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Journal of Nonlinear Science

, Volume 29, Issue 4, pp 1499–1522 | Cite as

Two Limit Cycles in Liénard Piecewise Linear Differential Systems

  • Jaume LlibreEmail author
  • Enrique Ponce
  • Clàudia Valls
Article
  • 146 Downloads

Abstract

Some techniques for studying the existence of limit cycles for smooth differential systems are extended to continuous piecewise linear differential systems. Rigorous new results are provided on the existence of two limit cycles surrounding the equilibrium point at the origin for systems with three zones separated by two parallel straight lines without symmetry. As a relevant application, it is shown the existence of bistable regimes in an asymmetric memristor-based electronic oscillator.

Keywords

Nonlinear control systems Periodic orbits Limit cycles Liénard piecewise linear differential systems 

Mathematics Subject Classification

Primary 34C05 Secondary 34C23 

Notes

Acknowledgements

J.L. is partially supported by the Ministerio de Economía, Industria y Competitividad, Agencia Estatal de Investigación Grant MTM2016-77278-P (FEDER), the Agència de Gestió d’Ajuts Universitaris i de Recerca Grant 2017 SGR 1617, and the European Project Dynamics-H2020-MSCA-RISE-2017-777911. E.P. was supported by MINECO/FEDER Grant MTM2015-65608-P and by the Consejería de Economía y Conocimiento de la Junta de Andalucía under Grant P12-FQM-1658. C.V. was partially supported by FCT - Fundação para a Ciência e a Tecnologia within the Project UID/MAT/04459/2013.

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Authors and Affiliations

  1. 1.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterra, BarcelonaSpain
  2. 2.Departamento de Matemática AplicadaEscuela Técnica Superior de IngenieríaSevilleSpain
  3. 3.Departamento de Matemática, Instituto Superior TécnicoUniversidade de LisboaLisboaPortugal

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