  In this paper, we propose a mean-field model which attempts to bridge the gap
between random Boolean networks and more realistic stochastic modeling of
genetic regulatory networks. The main idea of the model is to replace all
regulatory interactions to any one gene with an average or effective
interaction, which takes into account the repression and activation mechanisms.
We find that depending on the set of regulatory parameters, the model exhibits
rich nonlinear dynamics. The model also provides quantitative support to the
earlier qualitative results obtained for random Boolean networks.
