Complete bifurcation diagram and global phase portraits of Liénard differential equations of degree four

DOI10.1016/j.jmaa.2019.123802zbMath1482.34091OpenAlexW2997369424MaRDI QIDQ2304263

Hebai Chen, Xiaofeng Chen

Publication date: 9 March 2020

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2019.123802

zbMATH Keywords

bifurcationlimit cycleglobal phase portraitseparatrix loop

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

A nonsmooth van der Pol-Duffing oscillator. I: The sum of indices of equilibria is \(-1\) ⋮ A Quintic \(\boldsymbol{\mathbb{Z}_2}\)-Equivariant Liénard System Arising from the Complex Ginzburg–Landau Equation ⋮ Global-in-time existence of unbounded separatrices and blow-up time of solutions for Liénard systems whose restoring force is an odd power function ⋮ Phase portraits and bifurcation diagram of the Gray-Scott model

Cites Work

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• A proof of Wang-Kooij's conjectures for a cubic Liénard system with a cusp
• Global phase portrait of a degenerate Bogdanov-Takens system with symmetry
• Classical Liénard equations of degree \(n\geqslant 6\) can have \([\frac{n-1}{2}+2\) limit cycles]
• Uniqueness of limit cycles for Liénard differential equations of degree four
• Rotated vector fields
• On a four parameter family of planar vector fields
• Quadratic Liénard equations with quadratic damping
• Mathematical problems for the next century
• Global phase portraits of a degenerate Bogdanov-Takens system with symmetry. II
• Perturbation from an elliptic Hamiltonian of degree four. III: global centre.
• Perturbation from an elliptic Hamiltonian of degree four. IV: Figure eight-loop.
• Slow divergence integrals in classical Liénard equations near centers
• Limit cycles of the classical Liénard differential systems: a survey on the Lins Neto, de Melo and Pugh's conjecture
• A proof of Perko's conjectures for the Bogdanov-Takens system
• Dynamical analysis of a cubic Liénard system with global parameters (II)
• Dynamical analysis of a cubic Liénard system with global parameters
• Cubic Lienard equations with linear damping
• More limit cycles than expected in Liénard equations
• On the uniqueness of limit cycles surrounding one or more singularities for Liénard equations
• Limit Cycles in a Cubic System with a Cusp
• A Global Analysis of the Bogdanov–Takens System
• Global study of a family of cubic Liénard equations
• Homoclinic Loop and Multiple Limit Cycle Bifurcation Surfaces
• Perturbations from an elliptic Hamiltonian of degree four. II: Cuspidal loop
• Perturbations from an elliptic Hamiltonian of degree four. I: Saddle loop and two saddle cycles

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