Bifurcation analysis of a van der Pol-Duffing circuit with parallel resistor
type: Item
instance of: scholarly article
title: Bifurcation analysis of a van der Pol-Duffing circuit with parallel resistor
zbMATH Open document ID: 1184.94281
DOI: 10.1155/2009/149563
author: Denis De Carvalho Braga
author: Luis Fernando Mello
author: Marcelo Messias
published in: Mathematical Problems in Engineering
publication date: 2010-04-23T00:00:00Z
full work available at URL: https://eudml.org/doc/233082
review text: Summary: We study the local codimension one, two, and three bifurcations which occur in a recently proposed Van der Pol-Duffing circuit (ADVP) with parallel resistor, which is an extension of the classical Chua's circuit with cubic nonlinearity. The ADVP system presents a very rich dynamical behavior, ranging from stable equilibrium points to periodic and even chaotic oscillations. Aiming to contribute to the understand of the complex dynamics of this new system we present an analytical study of its local bifurcations and give the corresponding bifurcation diagrams. A complete description of the regions in the parameter space for which multiple small periodic solutions arise through the Hopf bifurcations at the equilibria is given. Then, by studying the continuation of such periodic orbits, we numerically find a sequence of period doubling and symmetric homoclinic bifurcations which leads to the creation of strange attractors, for a given set of the parameter values.
Mathematics Subject Classification ID: 94C05
Mathematics Subject Classification ID: 37N35
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 5700430
Wikidata QID: Q58648882
describes a project that uses: Mathematica
MaRDI profile type: Publication
OpenAlex ID: W2132550995
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description: scientific article; zbMATH DE number 5700430