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Página principal > Artículos > Artículos publicados > Melnikov analysis in nonsmooth differential systems with nonlinear switching manifold |
Fecha: | 2019 |
Resumen: | We study the family of piecewise linear differential systems in the plane with two pieces separated by a cubic curve. Our main result is that 7 is a lower bound for the Hilbert number of this family. In order to get our main result, we develop the Melnikov functions for a class of nonsmooth differential systems, which generalizes, up to order 2, some previous results in the literature. Whereas the first order Melnikov function for the nonsmooth case remains the same as for the smooth one (i. e. the first order averaged function) the second order Melnikov function for the nonsmooth case is different from the smooth one (i. e. the second order averaged function). We show that, in this case, a new term depending on the jump of discontinuity and on the geometry of the switching manifold is added to the second order averaged function. |
Ayudas: | Ministerio de Economía y Competitividad MTM2016-77278-P Ministerio de Economía y Competitividad MTM2013-40998-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-568 |
Derechos: | Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió acceptada per publicar |
Materia: | Melnikov theory ; Averaging theory ; Nonsmooth differential systems ; Piecewise linear differential systems ; Nonlinear switching manifold ; Limit cycles ; Hilbert number |
Publicado en: | Journal of differential equations, Vol. 267, Issue 6 (September 2019) , p. 3748-3767, ISSN 1090-2732 |
Postprint 23 p, 372.4 KB |