Bifurcations of multiple relaxation oscillations in polynomial Liénard equations

DOI10.1090/S0002-9939-2010-10610-XzbMath1230.37061OpenAlexW1971377732MaRDI QIDQ3005619

Freddy Dumortier, Peter De Maesschalck

Publication date: 9 June 2011

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-2010-10610-x

zbMATH Keywords

limit cyclessingular perturbationsslow-fast systemrelaxation oscillationelementary catastrophypolynomial Liénard equations

Mathematics Subject Classification ID

Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Relaxation oscillations for ordinary differential equations (34C26) Canard solutions to ordinary differential equations (34E17)

Related Items

Existence and uniqueness of limit cycles for generalized \(\phi\)-Laplacian Liénard equations, Studies of the Petrov module for a family of generalized Liénard integrable systems, Conditions for polynomial Liénard centers, Time and entry-exit relation near a planar turning point, Slow-fast Bogdanov-Takens bifurcations, Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}+2\) limit cycles], Center Conditions and Bifurcation of Limit Cycles Created from a Class of Second-Order ODEs, Bifurcations of Critical Periods for a Class of Quintic Liénard Equation, Asymptotic lower bounds on Hilbert numbers using canard cycles, Planar canards with transcritical intersections

Cites Work

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• Multiple canard cycles in generalized Liénard equations