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Stability of singular limit cycles for Abel equations
Bravo, Jose Luis
Fernández, Manuel
Gasull, Armengol

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 .
Drets: Tots els drets reservats.
Llengua: Anglès
Document: article ; recerca ; preprint
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

DOI: 10.3934/dcds.2015.35.1873

20 p, 413.0 KB

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Documents de recerca > Documents dels grups de recerca de la UAB > Centres i grups de recerca (producció científica) > Ciències > GSD (Grup de sistemes dinàmics)
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