Global phase portraits of a degenerate Bogdanov-Takens system with symmetry. II

DOI10.3934/dcdsb.2018130zbMath1405.34023OpenAlexW2587889626MaRDI QIDQ1756873

Xingwu Chen, Hebai Chen

Publication date: 27 December 2018

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.2018130

zbMATH Keywords

bifurcationlimit cycleglobal phase portraitdegenerate Bogdanov-Takens systemfigure-eight loop

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) 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) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (10)

A nonsmooth van der Pol-Duffing oscillator. I: The sum of indices of equilibria is \(-1\) ⋮ A nonsmooth van der Pol-Duffing oscillator. II: The sum of indices of equilibria is \(1\) ⋮ A Quintic \(\boldsymbol{\mathbb{Z}_2}\)-Equivariant Liénard System Arising from the Complex Ginzburg–Landau Equation ⋮ Dynamical behaviors of van der Pol-Duffing systems with indefinite degree ⋮ Nilpotent bi-center in continuous piecewise \(\mathbb{Z}_2\)-equivariant cubic polynomial Hamiltonian systems ⋮ The focus case of a nonsmooth Rayleigh-Duffing oscillator ⋮ The saddle case of Rayleigh-Duffing oscillators ⋮ Dynamical analysis of a cubic Liénard system with global parameters (III) ⋮ Complete bifurcation diagram and global phase portraits of Liénard differential equations of degree four ⋮ Global dynamics of a quintic Liénard system with Z2 -symmetry I: saddle case

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