Small-amplitude limit cycles in Liénard systems via multiplicity

DOI10.1006/jdeq.1999.3649zbMath0947.34014OpenAlexW2076924905MaRDI QIDQ1960913

Joan Torregrosa, Armengol Gasull

Publication date: 2 November 2000

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

Full work available at URL: https://doi.org/10.1006/jdeq.1999.3649

zbMATH Keywords

multiplicitylimit cyclesweak focuspolynomial Liénard systemLiénard equationsmaximum order of degeneracy

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 (20)

Hopf bifurcation for a \(\varphi \)-Laplacian Liénard system ⋮ HOPF BIFURCATIONS FOR NEAR-HAMILTONIAN SYSTEMS ⋮ Restricted independence in displacement function for better estimation of cyclicity ⋮ Small-amplitude limit cycles of polynomial Liénard systems ⋮ Small-amplitude limit cycles of certain planar differential systems ⋮ LIMIT CYCLES IN TWO TYPES OF SYMMETRIC LIÉNARD SYSTEMS ⋮ Successive bifurcations at infinity for second order O.D.E's. ⋮ Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs ⋮ Periodic travelling waves in nonlinear reaction-diffusion equations via multiple Hopf bifurcation ⋮ Generalized Liénard equations, cyclicity and Hopf-Takens bifurcations ⋮ The number of small amplitude limit cycles in arbitrary polynomial systems ⋮ Hopf bifurcation for two types of Liénard systems ⋮ Absolute cyclicity, Lyapunov quantities and center conditions ⋮ The applied geometry of a general Liénard polynomial system ⋮ Unnamed Item ⋮ A NOTE ON PERIODIC SOLUTIONS OF A FORCED LIÉNARD-TYPE EQUATION ⋮ Cyclicity of some Liénard systems ⋮ Center problem for several differential equations via Cherkas' method ⋮ Highest weak focus order for trigonometric Liénard equations ⋮ Small-amplitude limit cycles of some Liénard-type systems

Cites Work

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• Small-amplitude limit cycles of Liénard systems
• Center problem for several differential equations via Cherkas' method
• Generalized quadratic Liénard equations
• More results on the bifurcation of limit cycles for systems of Liénard type
• Small-amplitude limit cycles in polynomial Liénard systems
• Stability of motion
• The number of small-amplitude limit cycles of Liénard equations
• Order of cyclicity of the singular point of lineard's polynomial vector fields
• Small-amplitude limit cycles of certain Liénard systems
• Liénard systems and the second part of Hilbert's sixteenth problem

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