FORMAL DECOMPOSITION METHOD AND PARAMETRIC NORMAL FORMS

DOI10.1142/S0218127410027830zbMath1208.34046MaRDI QIDQ3086267

Majid Gazor, Pei Yu

Publication date: 30 March 2011

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

zbMATH Keywords

parametric normal formformal decompositiondegenerate nonlinear centerformal basis style

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 ordinary differential equations (34-04)

Related Items (10)

Normal form of Bogdanov-Takens: styles and a hypernormalization method ⋮ The infinite level normal forms for non-resonant double Hopf singularities ⋮ Spectral sequences and parametric normal forms ⋮ Normal Form Analysis of ℤ2-Equivariant Singularities ⋮ Parametric normal forms for Bogdanov-Takens singularity; the generalized saddle-node case ⋮ Bogdanov-Takens bifurcation in predator-prey systems ⋮ Bifurcation Control and Universal Unfolding for Hopf-Zero Singularities with Leading Solenoidal Terms ⋮ Bifurcation Controller Designs for the Generalized Cusp Plants of Bogdanov--Takens Singularity with an Application to Ship Control ⋮ Bifurcation Analysis of a Mosquito Population Model with a Saturated Release Rate of Sterile Mosquitoes ⋮ Complex dynamics in a unified SIR and HIV disease model: a bifurcation theory approach

Uses Software

• Maple

Cites Work

• Unique normal forms for vector fields and Hamiltonians
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• Hypernormal form theory: foundations and algorithms
• Unique normal forms: The nilpotent Hamiltonian case
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• Further reductions of normal forms for dynamical systems
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• Normal forms near critical points for differential equations and maps
• AN EFFICIENT METHOD FOR COMPUTING THE SIMPLEST NORMAL FORMS OF VECTOR FIELDS
• A SUFFICIENT CONDITION FOR THE UNIQUENESS OF NORMAL FORMS AND UNIQUE NORMAL FORMS OF GENERALIZED HOPF SINGULARITIES
• Normal forms for nonlinear vector fields. I. Theory and algorithm
• UNIQUE NORMAL FORMS FOR NILPOTENT PLANAR VECTOR FIELDS
• Normal Forms and Unfoldings for Local Dynamical Systems
• The simplest normal form of Hopf bifurcation
• INFINITE ORDER PARAMETRIC NORMAL FORM OF HOPF SINGULARITY
• SIMPLEST NORMAL FORMS OF HOPF AND GENERALIZED HOPF BIFURCATIONS
• Averaging methods in nonlinear dynamical systems

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