Stochastic stability and its application to the analysis of gene regulatory networks

Abstract—As gene regulatory network design and imple-mentation becomes more common, understanding the stochas-tic stability properties of these networks is increasingly be-coming more of a necessity. A study of such properties would uncover regimes of stable behavior under both cellular intrinsic biochemical noise, and extrinsic uncertainty resulting from fluctuating environments and noisy interconnections between individual networks. In this work, we revise and specialize common notions of stochastic stability to study two prototypical models of gene regulatory networks that have extensively been used in the biological literature. I