Bifurcation diagram and global phase portraits of a family of quadratic vector fields in class \(I\)

DOI10.1007/s12346-020-00402-4zbMath1446.34051OpenAlexW3033446541MaRDI QIDQ2190830

Yanyan Li

Publication date: 22 June 2020

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

Full work available at URL: https://doi.org/10.1007/s12346-020-00402-4

zbMATH Keywords

bifurcationsaddle connectionrotated vector fieldglobal phase portraitgeneralized normal sector

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) 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)

Related Items (1)

Dynamics of polynomial Rayleigh-Duffing system near infinity and its global phase portraits with a center

Cites Work

• Unnamed Item
• Unnamed Item
• A new class of quadratic systems
• The classification on the global phase portraits of two-dimensional Lotka-Volterra system
• Global behavior of limit cycles in rotated vector fields
• Quadratic systems with center and their perturbations
• Uniqueness of limit cycles of quadratic system (III)\(_{m=0}\)
• Global topological configurations of singularities for the whole family of quadratic differential systems
• Nonexistence of limit cycles for a class of structurally stable quadratic vector fields
• Limit cycles near hyperbolas in quadratic systems
• Qualitative theory of planar differential systems
• A survey of quadratic systems
• Topological Classification of Quadratic Polynomial Differential Systems with a Finite Semi-Elemental Triple Saddle
• Phase Portraits of Planar Quadratic Systems
• A Global Analysis of the Bogdanov–Takens System
• Structurally stable quadratic vector fields
• Centennial History of Hilbert's 16th Problem
• Structurally Unstable Quadratic Vector Fields of Codimension One
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Remarks on 16th weak Hilbert problem forn 2*
• The Geometry of Quadratic Differential Systems with a Weak Focus of Third Order
• Generalized normal sectors and orbits in exceptional directions
• Phase portraits of quadratic systems without finite critical points
• THE GEOMETRY OF QUADRATIC DIFFERENTIAL SYSTEMS WITH A WEAK FOCUS OF SECOND ORDER
• Phase portraits of quadratic systems with finite multiplicity one

This page was built for publication: Bifurcation diagram and global phase portraits of a family of quadratic vector fields in class \(I\)