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Bogdanov, R. "Bifurcations of a Limit Cycle for a Family of Vector Fields on the Plane." Selecta Math. Soviet 1, 373–388, 1981.
273:{\displaystyle {\begin{aligned}y_{1}'&=y_{2},\\y_{2}'&=\beta _{1}+\beta _{2}y_{1}+y_{1}^{2}\pm y_{1}y_{2}.\end{aligned}}}
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Takens, F. "Forced
Oscillations and Bifurcations." Comm. Math. Inst. Rijksuniv. Utrecht 2, 1–111, 1974.
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two, meaning that two parameters must be varied for the bifurcation to occur. It is named after
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There exist two codimension-three degenerate Takens–Bogdanov bifurcations, also known as
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at zero (assuming that some technical nondegeneracy conditions are satisfied).
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111:. All associated bifurcation curves meet at the Bogdanov–Takens bifurcation.
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Dumortier F., Roussarie R., Sotomayor J. and
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301:Elements of Applied Bifurcation Theory
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311:Bifurcations of Planar Vector Fields
303:. New York: Springer-Verlag, 1995.
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92:around that point has a double
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329:"Bogdanov–Takens Bifurcation"
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18:Bogdanov-Takens bifurcation
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339:: 1854.
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80:=
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