Construction of codimension one homoclinic cycles

A.J. Homburg, M. Kellner, J. Knobloch

Research output: Contribution to JournalArticleAcademicpeer-review


We give an explicit construction of families of Dm-equivariant polynomial vector fields in possessing a codimension one homoclinic cycle. The homoclinic cycle consists of m homoclinic trajectories all connected to the equilibrium at the origin. The constructed vector fields can provide a setting for a (numerical) bifurcation study of these homoclinic cycles, in particular for m equal to a multiple of 4, where the bifurcations form an open problem. © 2013 © 2013 Taylor & Francis.
Original languageEnglish
Pages (from-to)133-151
JournalDynamical Systems-an International Journal
Issue number1
Publication statusPublished - 2014


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