Asymptotic Expansion of the Heteroclinic Bifurcation for the Planar Normal Form of the 1:2 Resonance

DOI10.1142/S0218127416500176zbMath1334.34122OpenAlexW2279960653MaRDI QIDQ2800703

Luci Any Roberto, Paulo Ricardo da Silva, Joan Torregrosa

Publication date: 18 April 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127416500176

zbMATH Keywords

bifurcation diagramplanar systemshomoclinic connections

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Asymptotic expansions of solutions to ordinary differential equations (34E05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (3)

Computation of all the coefficients for the global connections in the \(\mathbb{Z}_2\)-symmetric Takens-Bogdanov normal forms ⋮ Global bifurcation studies of a cubic Liénard system ⋮ Global phase portraits of a degenerate Bogdanov-Takens system with symmetry. II

Cites Work

• Unnamed Item
• Explicit upper and lower bounds for the traveling wave solutions of Fisher-Kolmogorov type equations
• Bifurcation values for a family of planar vector fields of degree five
• Applications of centre manifold theory
• Elements of applied bifurcation theory.
• Bifurcation diagram and stability for a one-parameter family of planar vector fields
• A proof of Perko's conjectures for the Bogdanov-Takens system
• BIFURCATION CURVES OF LIMIT CYCLES IN SOME LIÉNARD SYSTEMS

This page was built for publication: Asymptotic Expansion of the Heteroclinic Bifurcation for the Planar Normal Form of the 1:2 Resonance