Set stability and synchronization of generalized asynchronous probabilistic Boolean networks with impulsive effects

This paper investigates the set stability of generalized asynchronous probabilistic Boolean networks (GAPBNs) with impulsive effects. To this end, an efficient algorithm is designed to determine the largest invariant set of a given set. A necessary and sufficient criterion is then derived to determine set stability of GAPBNs with impulsive effects. Subsequently, the global stability and synchronization of GAPBNs with impulsive effects were verified by selecting different sets. Finally, examples are given to illustrate the results on set stability and synchronization.