  Dynamical systems having many coexisting attractors present interesting
properties from both fundamental theoretical and modelling points of view. When
such dynamics is under bounded random perturbations, the basins of attraction
are no longer invariant and there is the possibility of transport among them.
Here we introduce a basic theoretical setting which enables us to study this
hopping process from the perspective of anomalous transport using the concept
of a random dynamical system with holes. We apply it to a simple model by
investigating the role of hyperbolicity for the transport among basins. We show
numerically that our system exhibits non-Gaussian position distributions,
power-law escape times, and subdiffusion. Our simulation results are reproduced
consistently from stochastic Continuous Time Random Walk theory.
