Critical point of tori collision in quasiperiodically forced systems

We report on a type of scaling behavior in quasiperiodically forced systems . On the parameter plane the critical point appears as a terminal point of the tori-collision bifurcation curve; its location is found numerically wit h high precision for two basic models, the forced supercritical circle map and the forced quadratic map. The hypothesis of universality, based on reno rmalization group arguments, is advanced to explain the observed scaling pr operties for the critical attractor and for the parameter plane arrangement in the neighborhood of the criticality.