  Glass networks are piecewise linear ODE systems that models an interactive
system where there are 'switching points': the underlying dynamic changes
qualitatively when a certain variable pass over a threshold. One of the most
well-studied class of models of the original Glass network are the cyclic
attractor in the orthants (a sequence of orthants where the flow from one
orthant to another is unanimous), which was first defined and analysed by Glass
and Pasternack in 1978. In that paper, the authors gave a complete
classification of the topological features of the flow in a full-rank cyclic
attractor, which is a cyclic attractor that cannot be contained in any sub-cube
in the graph of orthants.
  In this paper, we will extend the definition of cyclic attractor to one
generalisation of the Glass network, one that allows for multiple switching
points in each variables, and give a complete classification of the topological
features of the flow for any cyclic attractor, both in the extended network and
the original network, including non full-rank ones. We will show that in any
cyclic attractor, there is either a unique and asymptotically stable periodic
orbit, or that all periodic orbits are degenerated.
