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On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system

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Abstract

Applying new results from the averaging theory for continuous and discontinuous differential systems, we study the periodic solutions of two distinct versions of the Michelson differential system: a Michelson continuous piecewise linear differential system and a Michelson discontinuous piecewise linear differential system. The tools here used can be applied to general nonsmooth differential systems.

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Acknowledgements

We thank to the reviewer his/her comments which help us to improve the presentation of this paper. The first author is partially supported by the MINECO grants MTM 2016-77278-P and MTM2013-40998-P, an AGAUR grant number 2014 SGR-568, the grants FP7-PEOPLE-2012-IRSES 318999 and 316338. The first two authors are also supported by the CAPES grant number 88881.030454/2013-01 from the program CSF-PVE. The second author is partially supported by the joint projects FP7-PEOPLE-2012-IRSES numbers 316338, CNPq grant “Projeto Universal 472796/2013-5” and FAPESP grant number 2014/00304-2. The third author is supported by a FAPESP grant number 2012/22000-0.

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Authors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Catalonia, Spain

    Jaume Llibre

  2. Departamento de Matemática, ICMC-Universidade de São Paulo, Avenida Trabalhador São-carlense, 400, São Carlos, SP, 13566-590, Brazil

    Regilene Oliveira & Camila Ap. B. Rodrigues

Authors
  1. Jaume Llibre
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  2. Regilene Oliveira
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  3. Camila Ap. B. Rodrigues
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Corresponding author

Correspondence to Regilene Oliveira.

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Communicated by Pierangelo Marcati.

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Llibre, J., Oliveira, R. & Rodrigues, C.A.B. On the periodic solutions of the Michelson continuous and discontinuous piecewise linear differential system. Comp. Appl. Math. 37, 1550–1561 (2018). https://doi.org/10.1007/s40314-016-0413-x

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  • DOI: https://doi.org/10.1007/s40314-016-0413-x

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