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Center boundaries for planar piecewise-smooth differential equations with two zones
Buzzi, Claudio A. (Universidade Estadual Paulista (Brasil). Department of Mathematics)
Pazim, Rubens (Universidade Federal de Mato Grosso (Brasil). Inst. de Ciências Naturais Humanas e Sociais)
Pérez-González, Set (Universidade Estadual Paulista (Brasil). Department of Mathematics)

Date: 2017
Abstract: This paper is concerned with 1-parameter families of periodic solutions of piecewise smooth planar vector fields, when they behave like a center of smooth vector fields. We are interested in finding a separation boundary for a given pair of smooth systems in such a way that the discontinuous system, formed by the pair of smooth systems, has a continuum of periodic orbits. In this case we call the separation boundary as a center boundary. We prove that given a pair of systems that share a hyperbolic focus singularity p 0 , with the same orientation and opposite stability, and a ray Σ 0 with endpoint at the singularity p 0 , we can find a smooth manifold Ω such that Σ 0 ∪ p 0 ∪ Ω is a center boundary. The maximum number of such manifolds satisfying these conditions is five. Moreover, this upper bound is reached.
Note: Número d'acord de subvenció EC/FP7/2012/318999
Note: Agraïments: The first author is partially supported by Procad-Capes88881.068462/2014-01 and FAPESP2013/24541-0. The second author is partially supported by program CAPES/PDSE grant number 7038/2014-03 and CAPES/DS program number 33004153071P0. The third author is supported by program CAPES/PNPD grant number 1271113.
Rights: Tots els drets reservats.
Language: Anglès.
Document: article ; recerca ; submittedVersion
Subject: Limit cycles ; Non-smooth differential systems ; Piecewise linear differential system
Published in: Journal of Mathematical Analysis and Applications, Vol. 445 (2017) , p. 631-649, ISSN 0022-247X

DOI: 10.1016/j.jmaa.2016.07.022


preprint
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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 2017-11-28, last modified 2019-02-02



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