Boundary crisis in quasiperiodically forced systems

We study boundary crisis in quasiperiodically forced dissipative systems us ing the Henon map as a characteristic example. The crisis is due to a homoc linic tangency of the stable and unstable manifolds of an accessible invari ant circle of saddle type on the basin boundary of the attractor Numerical evidence shows that the type of boundary crisis can change as the saddle ci rcle loses its accessibility due to the quasiperiodic forcing. This implies the existence of codimension-two double crisis vertices where a curve of b oundary crisis and a curve of interior crisis meet. We argue that bifurcati on points of higher codimension must exist in the full parameter space. (C) 2000 Elsevier Science B.V. All rights reserved.