Abstract:

We investigate the two-dimensional dynamical systems occurring in the
network regulatory systems theory for specic choices of regulatory matrix screen and sigmoidal regulatory function screen screen The description of attracting sets is
provided. The attracting sets of regulatory matrix screen consist of
one and only one critical point with type stable focus. The second attracting
sets of regulatory matrix screen consist of one, two or three critical
points with types stable node, saddle or degenerate.