Configurations of limit cycles in Liénard equations

DOI10.1016/j.jde.2013.08.004zbMath1297.34043OpenAlexW1969923070MaRDI QIDQ2637799

Freddy Dumortier, Bartomeu Coll, Rafel Prohens

Publication date: 14 February 2014

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2013.08.004

zbMATH Keywords

Liénard systemplanar vector fieldlimit cycles configurationMorse polynomial function

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23)

Related Items (5)

Realization problems for limit cycles of planar polynomial vector fields ⋮ Phase portraits of piecewise linear continuous differential systems with two zones separated by a straight line ⋮ A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems ⋮ Cyclicity of some Liénard systems ⋮ Existence of solitary wave solutions for a nonlinear fifth-order KdV equation

Cites Work

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• Cyclicity of common slow-fast cycles
• Configurations of fans and nests of limit cycles for polynomial vector fields in the plane
• A class of vectorfields on \(S^ 2\) that are topologically equivalent to polynomial vectorfields
• Inverse problems for dynamical systems
• A characterization of the \(\omega\)-limit sets of planar continuous dynamical systems
• Polynomial Liénard equations near infinity
• Configurations of limit cycles and planar polynomial vector fields.
• Differentiable dynamical systems

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