LIMIT CYCLES IN TWO TYPES OF SYMMETRIC LIÉNARD SYSTEMS

DOI10.1142/S0218127407018300zbMath1151.34312MaRDI QIDQ3510227

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Publication date: 2 July 2008

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

Liénard systemnormal formHilbert's 16th problemsmall-amplitude limit cycleHilbert's number

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)

Related Items (11)

Bifurcation of a piecewise smooth cubic system via expansion of Melnikov function ⋮ Limit cycles of generalized Liénard polynomial differential systems via averaging theory ⋮ Small-amplitude limit cycles of polynomial Liénard systems ⋮ Bifurcations of small limit cycles in Liénard systems with cubic restoring terms ⋮ Nilpotent center conditions in cubic switching polynomial Liénard systems by higher-order analysis ⋮ Bifurcation set and number of limit cycles in \(Z_{2}\)-equivariant planar vector fields of degree 5 ⋮ Maximum Number of Small Limit Cycles in Some Rational Liénard Systems with Cubic Restoring Terms ⋮ Hopf bifurcation for two types of Liénard systems ⋮ The applied geometry of a general Liénard polynomial system ⋮ Cyclicity of some Liénard systems ⋮ Small-amplitude limit cycles of some Liénard-type systems

Cites Work

• Limit cycles in generalized Liénard systems
• Small-amplitude limit cycles in polynomial Liénard systems
• Small-amplitude limit cycles in Liénard systems via multiplicity
• The number of small-amplitude limit cycles of Liénard equations
• Small-amplitude limit cycles of certain Liénard systems
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
• LIMIT CYCLES IN HIGHLY NON-LINEAR DIFFERENTIAL EQUATIONS

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