BIFURCATION SCENARIO OF A THREE-DIMENSIONAL VAN DER POL OSCILLATOR
1993 ◽
Vol 03
(02)
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pp. 399-404
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Keyword(s):
Nonlinear self-excited oscillations are usually investigated for two-dimensional models. We extend the simplest and best known of these models, the van der Pol oscillator, to a three-dimensional one and study its dynamical behaviour by methods of bifurcation analysis. We find cusps and other local codimension 2 bifurcations. A homoclinic (i.e. global) bifurcation plays an important role in the bifurcation diagram. Finally it is demonstrated that chaos sets in. Thus the system belongs to the few three-dimensional autonomous ones modelling physical situations which lead to chaotic behavior.
2014 ◽
Vol 24
(06)
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pp. 1430017
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Keyword(s):
2021 ◽
Keyword(s):
1996 ◽
Vol 7
(1)
◽
pp. 3-19
◽
2012 ◽
Vol 7
(1)
◽
pp. 54-80
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Keyword(s):
Keyword(s):