THE FOLD-FLIP BIFURCATION

Abstract

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.