  For large coupled nonlinear systems, it is difficult to visualize the
high-dimensional phase space, which has been thoroughly studied in smaller
systems with regards to phenomena such as riddled basins. Here we propose a
method to reduce the phase space by defining a phase space cross section. The
method is applied to a system of dynamically coupled maps introduced by Ito &
Kaneko (Phys. Rev. Lett., 88, 028701, 2001 & Phys. Rev. E, 67, 046226, 2003).
We show that the transitions between phases of different synchronization
behaviour are not always sharp but can be characterized by fractal boundaries
in both phase and parameter space.
