A bifurcation analysis of a simple electronic circuit
type: Item
instance of: scholarly article
title: A bifurcation analysis of a simple electronic circuit
zbMATH Open document ID: 1064.34030
DOI: 10.1016/S1007-5704(03)00104-7
published in: Communications in Nonlinear Science and Numerical Simulation
publication date: 2004-11-18T00:00:00Z
review text: The authors present a bifurcation analysis of an electronic circuit with a three-dimensional state-space, displaying a cubic nonlinearity realized by a voltage-controlled resistor. They focus on parameter values yielding an equilibrium with an (index-2 nilpotent) double-zero eigenvalue in the linearization. The nonlinear analysis is performed via normal forms in the center manifold. They compute parameter values leading to a codimension-three degenerate Takens-Bogdanov bifurcation. Numerical computations of bifurcation sets are carried out for two nondegenerate, codimension-two Takens-Bogdanov bifurcations organizing saddle-node and Hopf bifurcations together with homoclinic connections; saddle-node bifurcations of periodic orbits stemming from a degenerate Hopf bifurcation can also be observed.
reviewed by: Ricardo Riaza
Mathematics Subject Classification ID: 34C60
Mathematics Subject Classification ID: 37G10
Mathematics Subject Classification ID: 34C23
zbMATH DE Number: 2116295
zbMATH Keywords: Takens-Bogdanov bifurcation
zbMATH Keywords: Electronic circuits
zbMATH Keywords: Normal forms
author: Antonio Algaba
author: Estanislao Gamero
author: Alejandro J. Rodríguez-Luis
describes a project that uses: AUTO
describes a project that uses: HomCont
MaRDI profile type: Publication
cites work: Computing simplest normal forms for the Takens-Bogdanov singularity
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description: scientific article; zbMATH DE number 2116295