Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields

DOI10.3934/dcdsb.2020145zbMath1471.34060arXiv1708.07959OpenAlexW3023592199MaRDI QIDQ2028974

Haihua Liang, Jianfeng Huang

Publication date: 3 June 2021

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1708.07959

zbMATH Keywords

limit cyclequasi-homogeneous vector fieldplanar autonomous differential system

Mathematics Subject Classification ID

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

Related Items (4)

On the cyclicity of quasi-homogeneous polynomial systems ⋮ On the number of limit cycles bifurcating from a quartic reversible center ⋮ A new Chebyshev criterion and its application to planar differential systems ⋮ Criteria on the existence of limit cycles in planar polynomial differential systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Periodic solutions for equation \(\dot x = A(t)x^m + B(t)x^n + C(t)x^l\) with \(A(t)\) and \(B(t)\) changing signs
• Limit cycles bifurcating from planar polynomial quasi-homogeneous centers
• Integrability of two dimensional quasi-homogeneous polynomial differential systems
• A new uniqueness criterion for the number of periodic orbits of Abel equations
• Algebraic and topological classification of the homogeneous cubic vector fields in the plane
• Classification of the centers, their cyclicity and isochronicity for a class of polynomial differential systems generalizing the linear systems with cubic homogeneous nonlinearities
• Limit cycles bifurcating from the period annulus of quasi-homogeneous centers
• On the cyclicity of weight-homogeneous centers
• Non-existence and uniqueness of limit cycles for planar polynomial differential systems with homogeneous nonlinearities
• Structural stability of planar semi-homogeneous polynomial vector fields. Applications to critical points and to infinity
• Structural stability of planar homogeneous polynomial vector fields: Applications to critical points and to infinity
• Phase portraits of planar semi-homogeneous vector fields. II
• Limit cycles of polynomial differential equations with quintic homogeneous nonlinearities
• Vector fields with homogeneous nonlinearities and many limit cycles
• A uniqueness criterion of limit cycles for planar polynomial systems with homogeneous nonlinearities
• Monodromy, center-focus and integrability problems for quasi-homogeneous polynomial systems
• Limit Cycles for a Class of Abel Equations
• The integrability problem for a class of planar systems
• Limit cycles of a class of polynomial systems
• A Note on the Number of Limit Cycles in Certain Two-Dimensional Systems
• Bifurcation of limit cycles and integrability of planar dynamical systems in complex form
• Phase portraits of planar semi-homogeneous vector fields-I
• Differential Equations Defined by the Sum of two Quasi-Homogeneous Vector Fields
• Limit cycles for vector fields with homogeneous components
• ON INTEGRABILITY OF DIFFERENTIAL EQUATIONS DEFINED BY THE SUM OF HOMOGENEOUS VECTOR FIELDS WITH DEGENERATE INFINITY

This page was built for publication: Limit cycles of planar system defined by the sum of two quasi-homogeneous vector fields