AN EFFICIENT METHOD FOR COMPUTING THE SIMPLEST NORMAL FORMS OF VECTOR FIELDS

DOI10.1142/S0218127403006418zbMath1067.34041OpenAlexW2024569618MaRDI QIDQ4653786

Yuan Yuan, Pei Yu

Publication date: 8 March 2005

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

Full work available at URL: https://doi.org/10.1142/s0218127403006418

zbMATH Keywords

Hopf bifurcationcomputer algebraMAPLErecursive algorithmefficient computationCNFB-T singularitySNF

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Normal forms for dynamical systems (37G05) Software, source code, etc. for problems pertaining to dynamical systems and ergodic theory (37-04) Software, source code, etc. for problems pertaining to ordinary differential equations (34-04)

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Uses Software

• Maple

Cites Work

• Linear grading function and further reduction of normal forms
• Further reduction of the Takens-Bogdanov normal form
• The existence of the heat flow of \(H\)-systems.
• Unique normal form of Bogdanov-Takens singularities
• Singularities of vector fields
• Normal forms for nonlinear vector fields. II. Applications
• Normal forms for nonlinear vector fields. I. Theory and algorithm
• Hypernormal Form for the Hopf-Zero Bifurcation
• SIMPLEST NORMAL FORMS OF HOPF AND GENERALIZED HOPF BIFURCATIONS
• COMPUTATION OF SIMPLEST NORMAL FORMS OF DIFFERENTIAL EQUATIONS ASSOCIATED WITH A DOUBLE-ZERO EIGENVALUE