THE FOLD-FLIP BIFURCATION
2004 ◽
Vol 14
(07)
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pp. 2253-2282
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Keyword(s):
The fold-flip bifurcation occurs if a map has a fixed point with multipliers +1 and -1 simultaneously. In this paper the normal form of this singularity is calculated explicitly. Both local and global bifurcations of the unfolding are analyzed by exploring a close relationship between the derived normal form and the truncated amplitude system for the fold-Hopf bifurcation of ODEs. Two examples are presented, the generalized Hénon map and an extension of the Lorenz-84 model. In the latter example the first-, second- and third-order derivatives of the Poincaré map are computed using variational equations to find the normal form coefficients.
2021 ◽
Vol 31
(1)
◽
pp. 013126
Keyword(s):
Keyword(s):
2014 ◽
Vol 24
(1)
◽
pp. 013122
◽
2007 ◽
Vol 221
(12)
◽
pp. 1701-1715
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