dc.contributor.author |
Bravo, Jose Luis |
dc.contributor.author |
Gasull, Armengol |
dc.contributor.author |
Fernández, Manuel |
dc.date |
2015 |
dc.identifier |
https://ddd.uab.cat/record/145334 |
dc.identifier |
urn:10.3934/dcds.2015.35.1873 |
dc.identifier |
urn:oai:ddd.uab.cat:145334 |
dc.identifier |
urn:gsduab:3755 |
dc.identifier |
urn:articleid:15535231v35n5p1873 |
dc.identifier |
urn:scopus_id:84919622710 |
dc.identifier |
urn:wos_id:000346487400005 |
dc.identifier |
urn:oai:egreta.uab.cat:publications/9f97c83b-c0b6-4c5f-aff1-fc1c4553f437 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
Ministerio de Ciencia y Tecnología MTM 2011-22751 |
dc.relation |
Ministerio de Ciencia y Tecnología MTM 2008-03437 |
dc.relation |
Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410 |
dc.relation |
Discrete and continuous dynamical systems. Series A ; Vol. 35 Núm. 5 (2015), p. 1873-1890 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
dc.subject |
Abel equation |
dc.subject |
Closed solution |
dc.subject |
Limit cycles |
dc.subject |
Periodic solutions |
dc.title |
Stability of singular limit cycles for Abel equations |
dc.type |
Article |
dc.description.abstract |
Agraïments: FEDER-Junta Extremadura grant number GR10060 |
dc.description.abstract |
We obtain a criterion for determining the stability of singular limit cycles of Abel equations x = A(t)x3 + B(t)x2 . This stability controls the possible saddle-node bifurcations of limit cycles. Therefore, studying the Hopf-like bifurcations at x = 0, together with the bifurcations at infinity of a suitable compactification of the equations, we obtain upper bounds of their number of limit cycles. As an illustration of this approach, we prove that the family x = at(t−tA )x3 +b(t−tB )x2 , with a, b > 0, has at most two positive limit cycles for any tB , tA . |