The fold-flip bifurcation

Yu A. Kuznetsov*, H. G.E. Meijer, L. Van Veen

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    39 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)2253-2282
    Number of pages30
    JournalInternational journal of bifurcation and chaos in applied sciences and engineering
    Issue number7
    Publication statusPublished - 1 Jan 2004


    • Bifurcations of fixed points
    • Center manifold
    • Normal forms

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