The number of limit cycles from the perturbation of a quadratic isochronous system with two switching lines

DOI10.3934/cpaa.2022047OpenAlexW4214817761MaRDI QIDQ2136187

Ai Ke, Wei Geng, Mao'an Han

Publication date: 10 May 2022

Published in: Communications on Pure and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/cpaa.2022047

zbMATH Keywords

limit cyclesbifurcationMelnikov functionpiecewise smooth systemisochronous system

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) 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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (2)

The 16th Hilbert problem for discontinuous piecewise linear differential systems separated by the algebraic curve \(y = x^n\) ⋮ On the number of limit cycles of planar piecewise smooth quadratic systems with focus-parabolic type critical point

Cites Work

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• Bifurcation of periodic orbits emanated from a vertex in discontinuous planar systems
• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
• On the limit cycles of perturbed discontinuous planar systems with 4 switching lines
• Bounding the number of zeros of certain abelian integrals
• Bifurcation methods of periodic orbits for piecewise smooth systems
• Limit cycles of differential equations
• On Hopf bifurcation in non-smooth planar systems
• Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations
• Limit cycle bifurcations of piecewise smooth near-Hamiltonian systems with a switching curve
• A linear estimate of the number of limit cycles for a piecewise smooth near-Hamiltonian system
• Averaging methods of arbitrary order, periodic solutions and integrability
• BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• Limit Cycles from Perturbing a Piecewise Smooth System with a Center and a Homoclinic Loop
• BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION
• ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD
• Picard–Fuchs Equation Applied to Quadratic Isochronous Systems with Two Switching Lines

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