Are the complex distributed genetic networks inherently oscillatory and chaotic?

Complex mRNA-protein networks with distributed regulation of gene transcription are often mimicked by random Boolean networks. According to this mapping, the gene-expression kinetics are expected to depend strongly on the network connectivity, $m$. Specifically, the kinetics are predicted to be oscillatory or chaotic for $m>2$. We analyze this problem in more detail by using an accurate model explicitly describing the mRNA-protein interplay with randomly organized transcriptional regulation. Contrary to the expectations, our mean-field calculations and Monte Carlo simulations performed for $m=1$, $2$ and $4$ show that oscillations and chaos are lacking irrespective of $m$.