Synchronization of asynchronous probabilistic boolean network

This paper researches the synchronization of asynchronous probabilistic Boolean network and synchronization theorems are provided. Inner synchronization and outer synchronization are considered, respectively. It should be pointed that synchronization theorems and corollaries with probability one and probabilities unequal to one are both taken into consideration. What’s more, the asynchronous multivalued Boolean network is also studied as an extension. Finally, some examples for asynchronous probabilistic Boolean network synchronizations are provided in the numerical simulation.