ISSN:
1573-269X
Schlagwort(e):
bifurcations
;
Hopf-pitchfork
;
van der Pol
;
Duffing
Quelle:
Springer Online Journal Archives 1860-2000
Thema:
Mathematik
Notizen:
Abstract We consider a modified van der Pol–Duffing electronic circuit,focusing on the case where a Hopf-pitchfork bifurcation takes places.The analysis of this bifurcation is a simple way to detect andcharacterize purely three-dimensional behaviour (an oscillatory regimein three variables, quasiperiodic motion, etc.). The normal formanalysis provides the classification of different kinds ofHopf-pitchfork bifurcation, organized according to some degeneratecases. One of these degenerate cases is analyzed, by considering acodimension-three unfolding of a reflectionally symmetric planar vectorfield. Later, the implications for three-dimensional flows arepresented. Unlike another degenerate Hopf-pitchfork bifurcationsexhibited by the system, the one studied here does not involvequasiperiodic behaviour, so that the complexity related to quasiperiodicmotion is not present.
Materialart:
Digitale Medien
URL:
http://dx.doi.org/10.1023/A:1008328027179
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