Symbolic computation for center manifolds and normal forms of Bogdanov bifurcation in retarded functional differential equations

DOI10.1016/j.na.2006.04.010zbMath1124.34046OpenAlexW1999495038MaRDI QIDQ876961

My Lhassan Hbid, Mohamed Ait Babram, Redouane Qesmi

Publication date: 19 April 2007

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2006.04.010

zbMATH Keywords

delaycenter manifoldBogdanov-Takens bifurcationretarded differential equation

Mathematics Subject Classification ID

Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Bifurcation theory of functional-differential equations (34K18) Invariant manifolds of functional-differential equations (34K19)

Related Items

Approximate formulas and algorithms for constructing central manifolds of dynamic systems ⋮ Two effective stability criteria for linear time-delay systems with complex coefficients ⋮ Codimension Bifurcation Analysis of a Modified Leslie–Gower Predator–Prey Model with Two Delays ⋮ The bifurcation study of 1:2 resonance in a delayed system of two coupled neurons ⋮ Symbolic computation of normal form for Hopf bifurcation in a retarded functional differential equation with unknown parameters ⋮ Explicit formulas for computing the normal form of Bogdanov-Takens bifurcation in delay differential equations

Uses Software

• Maple

Cites Work

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• Delay equations. Functional-, complex-, and nonlinear analysis
• Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
• Normal forms for retarded functional differential equations and applications to Bogdanov-Takens singularity
• A Maple program for computing a terms of a center manifold, and element of bifurcations for a class of retarded functional differential equations with Hopf singularity
• Normal forms for nonlinear vector fields. I. Theory and algorithm
• Introduction to Applied Nonlinear Dynamical Systems and Chaos
• Computational scheme of a center manifold for neutral functional differential equations

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