  Study of network dynamics is very active area in biological and social
sciences. However, the relationship between the network structure and the
attractors of the dynamics has not been fully understood yet. In this study, we
numerically investigated the role of degenerate self-loops on the attractors
and its basin size using the budding yeast cell-cycle network model. In the
network, all self-loops negatively surpress the node (self-inhibition loops)
and the attractors are only fixed points, i.e. point attractors. It is found
that there is a simple division rule of the state space by removing the
self-loops when the attractors consist only of point attractors. The point
attractor with largest basin size is robust against the change of the
self-inhibition loop. Furthermore, some limit cycles of period 2 appear as new
attractor when a self-activation loop is added to the original network. It is
also shown that even in that case, the point attractor with largest basin size
is robust.
