Open AccessBifurcation Analysis of a Van der Pol-Duffing Circuit with Parallel Resistor
Author(s) -
Denis de Carvalho Braga,
Luis Fernando Mello,
Marcelo Messias
Publication year - 2009
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2009/149563
Subject(s) - homoclinic orbit , attractor , homoclinic bifurcation , parameter space , van der pol oscillator , bifurcation , mathematics , period doubling bifurcation , pitchfork bifurcation , chaotic , duffing equation , numerical continuation , biological applications of bifurcation theory , mathematical analysis , bifurcation diagram , nonlinear system , physics , geometry , computer science , quantum mechanics , artificial intelligence
We study the local codimension one, two, and three bifurcations whichoccur in a recently proposed Van der Pol-Duffing circuit (ADVP) with parallelresistor, which is an extension of the classical Chua's circuit with cubic nonlinearity.The ADVP system presents a very rich dynamical behavior, ranging fromstable equilibrium points to periodic and even chaotic oscillations. Aiming to contributeto the understand of the complex dynamics of this new system we presentan analytical study of its local bifurcations and give the corresponding bifurcationdiagrams. A complete description of the regions in the parameter space forwhich multiple small periodic solutions arise through the Hopf bifurcations at theequilibria is given. Then, by studying the continuation of such periodic orbits,we numerically find a sequence of period doubling and symmetric homoclinic bifurcationswhich leads to the creation of strange attractors, for a given set of theparameter values
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