Computation of the simplest normal forms with perturbation parameters based on Lie transform and rescaling

DOI10.1016/S0377-0427(01)00573-8zbMath1019.65043OpenAlexW2145011665MaRDI QIDQ1612380

Pei Yu

Publication date: 22 August 2002

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0377-0427(01)00573-8

zbMATH Keywords

instabilitybifurcationnonlinear ordinary differential equationcomputer algebra systemLie transformationsingle zero singularityconventional normal formsimplest normal formsimplest normal forms

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (13)

The simplest parametrized normal forms of Hopf and generalized Hopf bifurcations ⋮ INFINITE ORDER PARAMETRIC NORMAL FORM OF HOPF SINGULARITY ⋮ A matching pursuit technique for computing the simplest normal forms of vector fields ⋮ Spectral sequences and parametric normal forms ⋮ Parametric normal forms for Bogdanov-Takens singularity; the generalized saddle-node case ⋮ Normal forms of vector fields with perturbation parameters and their application ⋮ The simplest normal form and its application to bifurcation control ⋮ Normal forms and nonlocal chaotic behavior in sprott systems ⋮ FORMAL DECOMPOSITION METHOD AND PARAMETRIC NORMAL FORMS ⋮ SIMPLEST NORMAL FORMS FOR PLANAR SYSTEMS ON EQUILIBRIUM MANIFOLDS ⋮ Computation of the simplest normal form of a resonant double Hopf bifurcation system with the complex normal form method ⋮ On the constructive algorithm for stability analysis of an equilibrium point of a periodic Hamiltonian system with two degrees of freedom in the case of combinational resonance ⋮ Limit cycles near a homoclinic loop by perturbing a class of integrable systems

Uses Software

• Maple

Cites Work

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• SIMPLEST NORMAL FORMS OF HOPF AND GENERALIZED HOPF BIFURCATIONS
• COMPUTATION OF SIMPLEST NORMAL FORMS OF DIFFERENTIAL EQUATIONS ASSOCIATED WITH A DOUBLE-ZERO EIGENVALUE

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