  The combination of complex networks and dynamic systems research is poised to
yield some of the most interesting theoretic and applied scientific results
along the forthcoming decades. The present work addresses a particularly
important related aspect, namely the quantification of how well separated can
the attractors be in dynamic systems underlined by four types of complex
networks (Erd\H{o}s-R\'enyi, Barab\'asi-Albert, Watts-Strogatz and as well as a
geographic model). Attention is focused on grandmother dynamic systems, where
each state variable (associated to each node) is used to represent a specific
prototype pattern (attractor). By assuming that the attractors spread their
influence among its neighboring nodes through a diffusive process, it is
possible to overlook the specific details of specific dynamics and focus
attention on the separability among such attractors. This property is defined
in terms of two separation indices (one individual to each prototype and the
other considering also the immediate neighborhood) reflecting the balance and
proximity to attractors revealed by the activation of the network after a
diffusive process. The separation index considering also the neighborhood was
found to be much more informative, while the best separability was observed for
the Watts-Strogatz and the geographic models. The effects of the involved
parameters on the separability were investigated by correlation and path
analyses. The obtained results suggest the special importance of some
measurements in underlying the relationship between topology and dynamics.
