An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system

DOI10.5817/AM2020-4-199OpenAlexW3094643571MaRDI QIDQ5140377

Makoto Hayashi

Publication date: 15 December 2020

Published in: Archivum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5817/am2020-4-199

zbMATH Keywords

Liénard systemlimit cycleBendixson-Dulac criterionalgebraic invariant curveBogdanov-Takens system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Relaxation oscillations for ordinary differential equations (34C26)

Cites Work

• Elements of applied bifurcation theory.
• On the nonexistence of the closed orbit for a Liénard system
• A proof of Perko's conjectures for the Bogdanov-Takens system
• Some results on homoclinic and heteroclinic connections in planar systems
• A Simple Proof for the Unicity of the Limit Cycle in the Bogdanov-Takens System
• A Global Analysis of the Bogdanov–Takens System
• On the uniqueness of limit cycle for certain Liénard systems without symmetry
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: An improvement of the non-existence region for limit cycles of the Bogdanov-Takens system