Bifurcation of limit cycles of the nongeneric quadratic reversible system with discontinuous perturbations

DOI10.1007/s11425-018-9405-4OpenAlexW2963029550WikidataQ127474823 ScholiaQ127474823MaRDI QIDQ2197822

Jihua Yang

Publication date: 1 September 2020

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.03107

zbMATH Keywords

Melnikov functionPicard-Fuchs equationquadratic reversible systemChebyshev space

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14) 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 (3)

On the number of limit cycles of a class of Liénard-Rayleigh oscillators ⋮ Limit Cycles from Hopf Bifurcation in Nongeneric Quadratic Reversible Systems with Piecewise Perturbations ⋮ Bifurcation of limit cycles of a piecewise smooth Hamiltonian system

Cites Work

• Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones
• Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system with a homoclinic loop
• On the number of limit cycles for a class of discontinuous quadratic differential systems
• Quadratic perturbations of quadratic codimension-four centers
• Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
• Perturbations of quadratic centers
• Note on limit cycles for \(m\)-piecewise discontinuous polynomial Liénard differential equations
• Limit cycles for discontinuous quadratic differential systems with two zones
• Averaging theory for discontinuous piecewise differential systems
• Limit cycles for \(m\)-piecewise discontinuous polynomial Liénard differential equations
• A linear estimate of the number of limit cycles for some planar piecewise smooth quadratic differential system
• Piecewise-smooth dynamical systems. Theory and applications
• Linear estimate on the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics
• Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
• Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop
• BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS
• Heteroclinic bifurcations in damped rigid block motion
• Linear estimate for the number of zeros of Abelian integrals with cubic Hamiltonians
• BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION
• On the Gause predator-prey model with a refuge: a fresh look at the history

This page was built for publication: Bifurcation of limit cycles of the nongeneric quadratic reversible system with discontinuous perturbations