Computation of Normal Forms of Differential Equations Associated with Non-Semisimple Zero Eigenvalues

DOI10.1142/S0218127498001868zbMath0942.34039OpenAlexW1983470043MaRDI QIDQ4941382

Qinsheng Bi, Pei Yu

Publication date: 28 August 2000

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

Full work available at URL: https://doi.org/10.1142/s0218127498001868

zbMATH Keywords

normal formsdifferential equationscenter manifold theoryexplicit formulassymbolic computer programs

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Theoretical approximation of solutions to ordinary differential equations (34A45) Invariant manifolds for ordinary differential equations (34C45)

Related Items

Computation of the normal form as well as the unfolding of the vector field with zero-zero-Hopf bifurcation at the origin ⋮ Normal form theory and spectral sequences. ⋮ Control of oscillations from the \(k\)-zero bifurcation ⋮ COMPUTATION OF SIMPLEST NORMAL FORMS OF DIFFERENTIAL EQUATIONS ASSOCIATED WITH A DOUBLE-ZERO EIGENVALUE ⋮ Symbolic computation of normal forms for semi-simple cases ⋮ Methods to reduce nonlinear mechanical systems for instability computation ⋮ Symbolic software development for computing the normal form of double Hopf bifurcation.

Uses Software

• Maple

Cites Work

• Local and global behavior near homoclinic orbits
• Versal deformation of a singular point of a vector field on the plane in the case of zero eigenvalues
• Non-linear bifurcation analysis of non-gradient systems
• Further reduction of the Takens-Bogdanov normal form
• Singularities of vector fields
• COMPUTATION OF NORMAL FORMS VIA A PERTURBATION TECHNIQUE
• Static and dynamic bifurcations associated with a double-zero eigenvalue
• Bifurcations associated with a three-fold zero eigenvalue