Advanced search
Start date
Betweenand
Related content
(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

New lower bound for the Hilbert number in piecewise quadratic differential systems

Full text
Author(s):
da Cruz, Leonardo P. C. [1] ; Novaes, Douglas D. [2] ; Torregrosa, Joan [1]
Total Authors: 3
Affiliation:
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona - Spain
[2] Univ Estadual Campinas, Dept Matemat, Rua Sergio Buarque de Holanda, 651, Cidade Univ, BR-13083859 Campinas, SP - Brazil
Total Affiliations: 2
Document type: Journal article
Source: Journal of Differential Equations; v. 266, n. 7, p. 4170-4203, MAR 15 2019.
Web of Science Citations: 3
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-p (n) the extension of the Hilbert number to degree n piecewise polynomial differential systems, then H-p (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. (C) 2018 Elsevier Inc. All rights reserved. (AU)

FAPESP's process: 16/11471-2 - Sliding motion in discontinuous dynamical systems: periodic solutions, homoclinic connections, and nonlinear sliding modes
Grantee:Douglas Duarte Novaes
Support Opportunities: Regular Research Grants