Global study of a family of cubic Lienard equations.

A.I. Khibnik, B. Krauskopf, C. Rousseau

Research output: Contribution to JournalArticleAcademicpeer-review


We derive the global bifurcation diagram of a three-parameter family of cubic Liénard systems. This family seems to have a universal character in that its bifurcation diagram (or parts of it) appears in many models from applications for which a combination of hysteretic and self-oscillatory behaviour is essential. The family emerges as a partial unfolding of a doubly degenerate Bogdanov-Takens point, that is. of the codimension-four singularity with nilpotent linear part and no quadratic terms in the normal form. We give a new presentation of a local four-parameter bifurcation diagram which is a candidate for the universal unfolding of this singularity.
Original languageEnglish
Pages (from-to)1505-1519
Issue number6
Publication statusPublished - 1998


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