  We explore the escape dynamics in open Hamiltonian systems with multiple
channels of escape continuing the work initiated in Part I. A thorough
numerical investigation is conducted distinguishing between trapped (ordered
and chaotic) and escaping orbits. The determination of the location of the
basins of escape towards the different escape channels and their correlations
with the corresponding escape periods of the orbits is undoubtedly an issue of
paramount importance. We consider four different cases depending on the
perturbation function which controls the number of escape channels on the
configuration space. In every case, we computed extensive samples of orbits in
both the configuration and the phase space by numerically integrating the
equations of motion as well as the variational equations. It was found that in
all examined cases regions of non-escaping motion coexist with several basins
of escape. The larger escape periods have been measured for orbits with initial
conditions in the vicinity of the fractal structure, while the lowest escape
rates belong to orbits with initial conditions inside the basins of escape. In
addition, we related the model potential with applications in the field of
reactive multichannel scattering. We hope that our numerical analysis will be
useful for a further understanding of the escape mechanism of orbits in open
Hamiltonian systems with two degrees of freedom.
