Bifurcations of limit cycles in Kukles systems of arbitrary degree with invariant ellipse

DOI10.1016/j.aml.2012.01.039zbMath1264.34075OpenAlexW2047305877MaRDI QIDQ712585

Eduardo Sáez, Ivan Szanto

Publication date: 17 October 2012

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2012.01.039

zbMATH Keywords

limit cycleinvariant algebraic curveLyapunov quantitiesKukles systemPoincaré-Melnikov integral

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) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Invariant manifolds for ordinary differential equations (34C45)

Related Items (3)

On the limit cycles of a class of Kukles type differential systems ⋮ Bifurcation of limit cycles for a family of perturbed Kukles differential systems ⋮ On the cubic Kukles systems with an algebraic limit cycle of degree two

Uses Software

• Mathematica
• Matlab

Cites Work

• Unnamed Item
• Limit cycles in Kukles systems of arbitrary degree with invariant ellipse
• On the shape of limit cycles that bifurcate from Hamiltonian centers
• Coexistence of limit cycles and invariant algebraic curves for a Kukles system
• Some unsolved problems in the theory of differential equations and mathematical physics

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