Home > Articles > Published articles > New lower bound for the Hilbert number in piecewise quadratic differential systems |
Date: | 2019 |
Abstract: | We study the number of limit cycles bifurcating from a piecewise quadratic system. All the differential systems considered are piecewise in two zones separated by a straight line. We prove the existence of 16 crossing limit cycles in this class of systems. If we denote by H (n) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then H (2)≥16. As fas as we are concerned, this is the best lower bound for the quadratic class. Moreover, in the studied cases, all limit cycles appear nested bifurcating from a period annulus of a isochronous quadratic center. |
Grants: | Ministerio de Economía y Competitividad MTM2016-77278-P Agència de Gestió d'Ajuts Universitaris i de Recerca 2017/SGR-1617 |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Non-smooth differential system ; Limit cycles in piecewise quadratic differential systems ; First and second order perturbations of isochronous quadratic systems ; Hilbert number for piecewise quadratic differential systems |
Published in: | Journal of differential equations, Vol. 266, Núm. 7 (March 2019) , p. 4170-4203, ISSN 1090-2732 |
Postprint 29 p, 594.7 KB |