Georgia Institute of Technology College of Sciences

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 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 thought a Poincaré section. We find some boundaries of Arnold tongues and indications of loss of normal hyperbolicity for this stable family. This is joint work with A. R. Humphries and B. Krauskopf.