Limit cycles in two kinds of quadratic reversible systems with non-smooth perturbations

DOI10.1007/s12346-021-00493-7zbMath1478.34038OpenAlexW3166457029MaRDI QIDQ2046953

Jihua Yang

Publication date: 19 August 2021

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s12346-021-00493-7

zbMATH Keywords

limit cycleMelnikov functionPicard-Fuchs equationquadratic reversible differential system

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)

Cites Work

• Unnamed Item
• Unnamed Item
• Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems
• Limit cycle bifurcations in a class of perturbed piecewise smooth systems
• Bifurcation of periodic orbits emanated from a vertex in discontinuous planar systems
• 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
• Limit cycles for continuous and discontinuous perturbations of uniform isochronous cubic centers
• On the limit cycles of perturbed discontinuous planar systems with 4 switching lines
• Limit cycle bifurcations for piecewise smooth integrable differential systems
• Perturbations of quadratic centers of genus one
• Quadratic systems with center and their perturbations
• Note on limit cycles for \(m\)-piecewise discontinuous polynomial Liénard differential equations
• Piecewise linear differential system with a center-saddle type singularity
• Limit cycle bifurcations by perturbing non-smooth Hamiltonian systems with 4 switching lines via multiple parameters
• Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations
• Averaging theory of arbitrary order for piecewise smooth differential systems and its application
• Limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems
• Limit cycles for discontinuous quadratic differential systems with two zones
• Averaging theory for discontinuous piecewise differential systems
• On the abelian integrals of quadratic reversible centers with orbits formed by genus one curves of higher degree
• Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones
• Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems
• Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves
• Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop
• BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS
• The Maximal Number of Limit Cycles in Perturbations of Piecewise Linear Hamiltonian Systems with Two Saddles
• BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION

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