Web of Science: 4 citations, Scopus: 4 citations, Google Scholar: citations
Piecewise smooth dynamical systems: Persistence of periodic solutions and normal forms
Gouveia, Marcio R. A. (IBILCE-UNESP(Brazil). Departamento de Matemática)
Llibre, Jaume (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Novaes, Douglas D. (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
Pessoa, Claudio (IBILCE-UNESP(Brazil). Departamento de Matemática)

Date: 2016
Abstract: We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane \Sigma which admits an invariant hyperplane \Omega transversal to \Sigma containing a period annulus A fulfilled by crossing periodic solutions. For small discontinuous perturbations of these systems we develop a Melnikov-like function to control the persistence of periodic solutions contained in A. When n = 3 we provide normal forms for the piecewise linear case. Finally we apply the Melnikov-like function to study discontinuous perturbations of the given normal forms.
Note: Agraïments: The first and fourth author are partially supported by a FAPESP grant 2013/34541-0. The first and fourth authors are supported by a CAPES PROCAD grant 88881.068462/2014-01. The second author is partially supported by a CAPES CSF-PVE grant 88881.030454/ 2013-01. The third author is supported by a FAPESP grant 2015/02517-6.
Note: Número d'acord de subvenció MINECO/MTM2013-40998-P
Note: Número d'acord de subvenció AGAUR/2014/SGR-568
Note: Número d'acord de subvenció EC/FP7/2012/316338
Note: Número d'acord de subvenció EC/FP7/2012/316339
Rights: Tots els drets reservats.
Language: Anglès
Document: article ; recerca ; acceptedVersion
Subject: Crossing periodic orbits ; Limit cycle ; Lyapunov-Schmidt reduction ; Piecewise differential system
Published in: Journal of differential equations, Vol. 260 (2016) , p. 6108-6129, ISSN 1090-2732

DOI: 10.1016/j.jde.2015.12.034


Postprint
23 p, 542.3 KB

The record appears in these collections:
Research literature > UAB research groups literature > Research Centres and Groups (scientific output) > Experimental sciences > GSD (Dynamical systems)
Articles > Research articles
Articles > Published articles

 Record created 2017-01-23, last modified 2020-11-01



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