Center boundaries for planar piecewise-smooth differential equations with two zones

Autor: Rubens Pazim, Set Pérez-González, Claudio A. Buzzi
Rok vydání: 2017
Předmět:
Zdroj: Dipòsit Digital de Documents de la UAB
Universitat Autònoma de Barcelona
Recercat: Dipósit de la Recerca de Catalunya
Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Recercat. Dipósit de la Recerca de Catalunya
instname
ISSN: 0022-247X
3300-4153
DOI: 10.1016/j.jmaa.2016.07.022
Popis: 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. 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.
Databáze: OpenAIRE
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