Scaling Properties of Saddle-Node Bifurcations on Fractal Basin Boundaries

Given a chaotic attractor in a dynamical system with dense periodic windows (i.e., structurally unstable), is it possible to find a periodic driver that will phase synchronize the chaotic attractor? We conjecture that the answer is typically yes, and we give an example for a funneling chaotic attractor in the Roessler system.