Transcritical bifurcation at infinity in planar piecewise polynomial differential systems with two zones

DOI10.1080/14689367.2022.2092454OpenAlexW4283780929WikidataQ114098675 ScholiaQ114098675MaRDI QIDQ5048918

Luis Fernando Mello, Jaume Llibre, Denis de Carvalho Braga

Publication date: 16 November 2022

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689367.2022.2092454

zbMATH Keywords

limit cycletranscritical bifurcationPoincaré compactificationpiecewise differential system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Stability theory for smooth dynamical systems (37C75)

Cites Work

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• On a class of complete polynomial vector fields in the plane
• Hopf bifurcation from infinity for planar control systems
• On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems
• On the Lambert \(w\) function
• Limit cycles in a family of discontinuous piecewise linear differential systems with two zones in the plane
• Complex Analysis and Differential Equations
• Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields
• Introduction to the Qualitative Theory of Differential Systems

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