The limit cycles of Liénard equations in the strongly nonlinear regime

DOI10.1016/S0960-0779(98)00189-1zbMath0954.34021arXivnlin/0205027OpenAlexW1507550642MaRDI QIDQ1573913

José Luis López, Ricardo López-Ruiz

Publication date: 9 August 2000

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0205027

zbMATH Keywords

limit cycleLiénard equation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (12)

Number and amplitude of limit cycles emerging from topologically equivalent perturbed centers. ⋮ The homotopy analysis method and the Liénard equation ⋮ Simplified Liénard equation by homotopy analysis method ⋮ Sufficient conditions for the existence of at least \(n\) or exactly \(n\) limit cycles for the Liénard differential systems ⋮ Approximating the amplitude and form of limit cycles in the weakly nonlinear regime of Liénard systems ⋮ Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity ⋮ Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic ⋮ Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic ⋮ On some open problems in planar differential systems and Hilbert's 16th problem ⋮ BIFURCATION CURVES OF LIMIT CYCLES IN SOME LIÉNARD SYSTEMS ⋮ EXTENSION OF CHICONE'S METHOD FOR PERTURBATION SYSTEMS OF THREE PARAMETERS WITH APPLICATION TO THE LIENARD SYSTEM ⋮ Piecewise-linearized methods for oscillators with limit cycles

Cites Work

• Periodic motions
• The limit cycle of the van der Pol equation is not algebraic
• Liénard systems with several limit cycles
• Relaxation oscillations
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