Codimension Two Bifurcation Observed in a Phase Converter Circuit

Hiroyuki KITAJIMA  Tetsuya YOSHINAGA  Hiroshi KAWAKAMI  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E79-A   No.10   pp.1563-1567
Publication Date: 1996/10/25
Online ISSN: 
DOI: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Nonlinear Theory and its Applications (NOLTA))
Category: Nonlinear Circuits and Bifurcation
Keyword: 
codimension two bifurcation,  codimension three bifurcation,  coupled system,  nonlinear dynamical system,  

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Summary: 
We investigate bifurcations of the periodic solution observed in a phase converter circuit. The system equations can be considered as a nonlinear coupled system with Duffing's equation and an equation describing a parametric excitation circuit. In this system there are two types of solutions. One is with x = y = 0 which is the same as the solution of Duffing's equation (correspond to uncoupled case), another solution is with xy0. We obtain bifurcation sets of both solutions and discuss how does the coupling change the bifurcation structure. From numerical analysis we obtain a codimension two bifurcation which is intersection of double period-doubling bifurcations. Pericdic solutions generated by these bifurcations become chaotic states through a cascade of codimension three bifurcations which are intersections of D-type of branchings and period-doubling bifurcations.