Global phase portraits of the generalized van der Pol systems

DOI10.1016/J.BULSCI.2022.103213OpenAlexW4310076681MaRDI QIDQ2683686

Jaume Llibre, Claudia Valls

Publication date: 14 February 2023

Published in: Bulletin des Sciences Mathématiques (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.bulsci.2022.103213

zbMATH Keywords

centerLyapunov constantblow upsPoincaré compactificationvan der Pol systems

Mathematics Subject Classification ID

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

Cites Work

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• From canards of folded singularities to torus canards in a forced van der Pol equation
• Complex periodic bursting structures in the Rayleigh-van der Pol-Duffing oscillator
• Qualitative theory of planar differential systems
• A general equation for relaxation oscillations
• A nonsmooth van der Pol-Duffing oscillator. I: The sum of indices of equilibria is \(-1\)
• A nonsmooth van der Pol-Duffing oscillator. II: The sum of indices of equilibria is \(1\)
• A SURVEY ON THE BLOW UP TECHNIQUE
• Invariant manifolds

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