Dynamics of a delay equation with two state dependent delays

Renato Calleja
IIMAS-UNAM

We present a numerical study of the dynamics of a state-dependent delay equation with two state dependent delays that are linear in the state. In particular, we study some of the dynamical behavior driven by the existence of two-parameter families of invariant tori. A formal normal form analysis predicts the existence of torus bifurcations and the appearance of a two parameter family of stable invariant tori. We investigate the dynamics on the torus through a Poincaré section. We find Arnold tongues and indications of loss of normal hyperbolicity for this stable family. This is joint work with A. R. Humphries and B. Krauskopf.