Geometric tools to determine the hyperbolicity of limit cycles

DOI10.1016/j.jmaa.2006.09.012zbMath1135.34024OpenAlexW2092006040MaRDI QIDQ878468

Antoni Guillamon, Sabatini, Marco

Publication date: 26 April 2007

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2006.09.012

zbMATH Keywords

limit cycleshyperbolicityLiénard systemsLie brackets

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Stability of solutions to ordinary differential equations (34D20) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30)

Related Items (3)

Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms ⋮ Limit cycles uniqueness for second order ODE's polynomial in \(\dot x\) ⋮ The number of limit cycles in planar systems and generalized Abel equations with monotonous hyperbolicity

Cites Work

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• On period functions of Liénard systems
• Non-existence, uniqueness of limit cycles and center problem in a system that includes predator-prey systems and generalized Liénard equations
• A new criterion for controlling the number of limit cycles of some generalized Liénard equations
• First derivative of the period function with applications
• Limit cycles and Lie symmetries
• On the generalized Lienard equation with negative damping
• On the period function of planar systems with unknown normalizers

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