Discretizing bifurcation Diagrams Near codimension Two Singularities

We consider parameter-dependent, continuous-time dynamical systems under discretizations. It is shown that fold-Hopf singularities are O(hp)-shifted and turned into fold-Neimark-Sacker 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.

• Type: Journal
• Year: 2010
• Where: IJBC
• Authors: Páez Chávez Joseph
• Keywords: Continuous-time Dynamical Systems, Fold-Hopf Singularities, IJBC 2010, Local Bifurcation Diagram