Stability of Probabilistic Boolean Networks*

This paper studies the fix-point stability and set stability of Probabilistic Boolean networks based on its corresponding discrete Markov chain. Through the state classification of the corresponding Markov chain, necessary and sufficient conditions for the fix-point stability and set stability of Probabilistic Boolean networks are given seperately. And the method to find the largest invariant subset of Probabilistic Boolean networks is provided. Finally, numericial examples are given to illustrate the obtained theoretical results.