Discretizing bifurcation diagrams near codimension two singularities

Abstract:

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that fold-Hopf singularities are O(h p)-shifted and turned into fold-NeimarkSacker points by one-step methods of order p. Then we analyze the effect of discretizations methods on the local bifurcation diagram near BogdanovTakens and fold-Hopf singularities. In particular, we prove that the discretized codimension one curves intersect at the singularities in a generic manner. The results are illustrated by a numerical example. © 2010 World Scientific Publishing Company.

Año de publicación:

2010

Keywords:

Fuente:

scopus

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