Upper bounds for the number of limit cycles through linear differential equations

DOI10.2140/pjm.2006.226.277zbMath1135.34027OpenAlexW2015610311MaRDI QIDQ997109

Armengol Gasull, Hector J. Giacomini

Publication date: 20 July 2007

Published in: Pacific Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2140/pjm.2006.226.277

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07)

Related Items (13)

New criteria for the existence and non-existence of limit cycles in Liénard differential systems ⋮ On a Dulac function for the Kukles system ⋮ Global algebraic Poincaré-Bendixson annulus for the van der Pol system ⋮ Transversal curves for finding the exact number of limit cycles ⋮ New criterions on stability and order of analytic nilpotent foci ⋮ On the uniqueness of limit cycles in second-order oscillators ⋮ Limit cycles of polynomial Liénard systems via the averaging method ⋮ Bifurcation values for a family of planar vector fields of degree five ⋮ Effectiveness of the Bendixson-Dulac theorem ⋮ A note on the existence and construction of Dulac functions ⋮ Some open problems in low dimensional dynamical systems ⋮ Transversal conics and the existence of limit cycles ⋮ Some Applications of the Extended Bendixson-Dulac Theorem

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