Note on limit cycles for \(m\)-piecewise discontinuous polynomial Liénard differential equations

DOI10.1007/s00033-017-0844-2zbMath1379.34021OpenAlexW2744176216MaRDI QIDQ1684451

Changjian Liu, Guangfeng Dong

Publication date: 8 December 2017

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-017-0844-2

zbMATH Keywords

limit cycleaveraging methodLiénard differential systempiecewise differential system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Averaging method for ordinary differential equations (34C29) Discontinuous ordinary differential equations (34A36)

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Limit cycles appearing from the perturbation of differential systems with multiple switching curves, Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones, Bifurcation of limit cycles of the nongeneric quadratic reversible system with discontinuous perturbations, On the Number of Limit Cycles of Discontinuous Liénard Polynomial Differential Systems, ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION, Limit cycles in two kinds of quadratic reversible systems with non-smooth perturbations, Limit cycle bifurcations from a quadratic center with two switching lines, Limit cycles of piecewise polynomial differential systems with the discontinuity line \(xy = 0\), Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary, On the Hilbert number for piecewise linear vector fields with algebraic discontinuity set

Cites Work

• On nonsmooth perturbations of nondegenerate planar centers
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• Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones
• Averaging theory for discontinuous piecewise differential systems
• Limit cycles for \(m\)-piecewise discontinuous polynomial Liénard differential equations
• Piecewise-smooth dynamical systems. Theory and applications