Limit cycles and global dynamic of planar cubic semi-quasi-homogeneous systems

DOI10.3934/dcdsb.2021049zbMath1495.34053OpenAlexW3126310256MaRDI QIDQ2064503

Yanyan Li

Publication date: 6 January 2022

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

Full work available at URL: https://doi.org/10.3934/dcdsb.2021049

zbMATH Keywords

limit cyclesglobal phase portraitssemi-quasi-homogeneoustopologically equivalentplanar cubic systems

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) Equivalence and asymptotic equivalence of ordinary differential equations (34C41)

Related Items (2)

Probability of existence of limit cycles for a family of planar systems ⋮ Double homoclinic bifurcations by perturbing a class of cubic \(\mathrm{Z}_2\)-equivariant polynomial systems with nilpotent singular points

Cites Work

• Unnamed Item
• Unnamed Item
• Center of planar quintic quasi-homogeneous polynomial differential systems
• Integrability of two dimensional quasi-homogeneous polynomial differential systems
• Limit cycles for planar semi-quasi-homogeneous polynomial vector fields
• Classification of global phase portraits of planar quartic quasi-homogeneous polynomial differential systems
• On the centers of the weight-homogeneous polynomial vector fields on the plane
• Polynomial first integrals for weight-homogeneous planar polynomial differential systems of weight degree 3
• Algebraic and topological classification of the homogeneous cubic vector fields in the plane
• Classification of global phase portrait of planar quintic quasi-homogeneous coprime polynomial systems
• Cyclicity of a family of vector fields
• Phase portraits of planar semi-homogeneous vector fields. III
• Phase portraits of planar semi-homogeneous vector fields. II
• Planar semi-quasi homogeneous polynomial differential systems with a given degree
• Planar quasi-homogeneous polynomial differential systems and their integrability
• Centers of quasi-homogeneous polynomial differential equations of degree three
• Qualitative theory of planar differential systems
• Limit cycles for vector fields with homogeneous components

This page was built for publication: Limit cycles and global dynamic of planar cubic semi-quasi-homogeneous systems