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Pàgina inicial > Articles > Articles publicats > Stability of singular limit cycles for Abel equations |
Data: | 2015 |
Resum: | 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 . |
Ajuts: | Ministerio de Ciencia y Tecnología MTM 2011-22751 Ministerio de Ciencia y Tecnología MTM 2008-03437 Agència de Gestió d'Ajuts Universitaris i de Recerca 2014/SGR-410 |
Nota: | Agraïments: FEDER-Junta Extremadura grant number GR10060 |
Drets: | Tots els drets reservats. |
Llengua: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Matèria: | Abel equation ; Closed solution ; Limit cycles ; Periodic solutions |
Publicat a: | Discrete and continuous dynamical systems. Series A, Vol. 35 Núm. 5 (2015) , p. 1873-1890, ISSN 1553-5231 |
Postprint 20 p, 413.0 KB |