Fixed and moving limit cycles for Liénard equations

DOI10.1007/s10231-019-00850-zzbMath1453.34039OpenAlexW2938125615MaRDI QIDQ2009072

Armengol Gasull, Sabatini, Marco

Publication date: 27 November 2019

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10231-019-00850-z

zbMATH Keywords

limit cyclebifurcationsinvariant algebraic curveLiénard equation

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) 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) Periodic orbits of vector fields and flows (37C27)

Related Items (4)

On the existence and uniqueness of limit cycles for hybrid oscillators ⋮ Global dynamics of a Wilson polynomial Liénard equation ⋮ Effectiveness of the Bendixson-Dulac theorem ⋮ Darboux first integrals and linearizability of quadratic-quintic Duffing-van der Pol oscillators

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bifurcation values for a family of planar vector fields of degree five
• Rotated vector fields
• A note on: ``Relaxation oscillators with exact limit cycles
• Polynomial Liénard equations near infinity
• Relaxation oscillators with exact limit cycles
• Algebraic approximations to bifurcation curves of limit cycles for the Liénard equation
• Multiplicity of limit cycles and analytic \(m\)-solutions for planar differential systems
• On the stability of limit cycles for planar differential systems
• Qualitative theory of planar differential systems
• Invariant algebraic curves for the cubic Liénard system with linear damping
• On the generalized Lienard equation with negative damping
• Limit-cycles and rotated vector fields
• Some Applications of the Extended Bendixson-Dulac Theorem
• On the hyperelliptic limit cycles of Liénard systems
• An effective method of counting the number of limit cycles
• A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
• Algebraic invariant curves for the Liénard equation
• Global Families of Limit Cycles of Planar Analytic Systems

This page was built for publication: Fixed and moving limit cycles for Liénard equations