On the number of limit cycles for a class of discontinuous quadratic differential systems

DOI10.1016/j.jmaa.2016.11.033zbMath1360.34073arXiv1609.08048OpenAlexW2963636951MaRDI QIDQ504853

Shimin Li, Xiuli Cen, Yulin Zhao

Publication date: 17 January 2017

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.08048

zbMATH Keywords

isochronous centerlimit cycleaveraging methoddiscontinuous differential systemChebyshev criterion

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36)

Related Items (13)

Bifurcation methods of periodic orbits for piecewise smooth systems ⋮ Bifurcation of limit cycles of the nongeneric quadratic reversible system with discontinuous perturbations ⋮ Bifurcation of limit cycles in a family of piecewise smooth systems via averaging theory ⋮ ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD ⋮ Cyclicity of a Class of Hamiltonian Systems under Perturbations of Piecewise Smooth Polynomials ⋮ ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION ⋮ Limit cycles for a discontinuous quintic polynomial differential system ⋮ Limit cycles of a Liénard system with symmetry allowing for discontinuity ⋮ On the number of limit cycles for a class of piecewise smooth Hamiltonian systems with discontinuous perturbations ⋮ Limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems ⋮ Limit cycle bifurcations from a quadratic center with two switching lines ⋮ Picard–Fuchs Equation Applied to Quadratic Isochronous Systems with Two Switching Lines ⋮ Limit Cycles of a Kind of Nonsmooth Differential Systems with Two Switching Lines

Cites Work

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• Limit cycles coming from some uniform isochronous centers
• Bounding the number of zeros of certain abelian integrals
• Bifurcation of limit cycles from quadratic isochrones
• Quadratic perturbations of quadratic codimension-four centers
• Averaging methods for finding periodic orbits via Brouwer degree.
• On the birth of limit cycles for non-smooth dynamical systems
• Limit cycles for discontinuous quadratic differential systems with two zones
• On the number of limit cycles in quadratic perturbations of quadratic codimension-four centres
• Bifurcation of critical periods from Pleshkan's isochrones
• Linear estimate for the number of zeros of Abelian integrals for quadratic isochronous centres
• Averaging methods in nonlinear dynamical systems

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