  Modeling gene regulatory networks (GRNs) is an important topic in systems
biology. Although there has been much work focusing on various specific
systems, the generic behavior of GRNs with continuous variables is still
elusive. In particular, it is not clear typically how attractors partition
among the three types of orbits: steady state, periodic and chaotic, and how
the dynamical properties change with network's topological characteristics. In
this work, we first investigated these questions in random GRNs with different
network sizes, connectivity, fraction of inhibitory links and transcription
regulation rules. Then we searched for the core motifs that govern the dynamic
behavior of large GRNs. We show that the stability of a random GRN is typically
governed by a few embedding motifs of small sizes, and therefore can in general
be understood in the context of these short motifs. Our results provide
insights for the study and design of genetic networks.
