Small-amplitude limit cycles of some Liénard-type systems

DOI10.1016/j.na.2009.09.011zbMath1279.34046OpenAlexW2079444102MaRDI QIDQ1044518

Jiao Jiang, Mao'an Han

Publication date: 18 December 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2009.09.011

zbMATH Keywords

limit cycleHopf bifurcationLiénard equation

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 ⋮ Hopf bifurcation for a \(\varphi \)-Laplacian Liénard system ⋮ Small-amplitude limit cycles of polynomial Liénard systems ⋮ Small-amplitude limit cycles of certain planar differential 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 ⋮ On necessary conditions for global asymptotic stability of equilibrium for the Liénard equation ⋮ Maximum Number of Small Limit Cycles in Some Rational Liénard Systems with Cubic Restoring Terms ⋮ The number of small amplitude limit cycles in arbitrary polynomial systems ⋮ Hopf bifurcation for two types of Liénard systems ⋮ Cyclicity of some Liénard systems

Cites Work

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• 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
• LIMIT CYCLES IN TWO TYPES OF SYMMETRIC LIÉNARD SYSTEMS
• Small-amplitude limit cycles of certain Liénard systems
• Small-amplitude limit cycle bifurcations for Liénard systems with quadratic or cubic damping or restoring forces
• Bifurcation Theory and Methods of Dynamical Systems
• LIMIT CYCLES IN HIGHLY NON-LINEAR DIFFERENTIAL EQUATIONS

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