Set reachability and set stability of Boolean networks with state‐dependent asynchronous updating rule

Abstract

AbstractAsynchronous behavior is significant for real biological systems. This paper explores the impact of state‐dependent asynchronous updating rule (SDAUR) on the set reachability and set stability of Boolean networks (BNs). First, a set of state‐dependent control variables is introduced to describe the SDAUR. Second, a new asynchronous set reachablity matrix is constructed based on an auxiliary input and semi‐tensor product. Third, using the asynchronous set reachablity matrix, several necessary and sufficient conditions are obtained for the set reachablity and set stability of BNs with SDAUR. Finally, the new results proposed in this paper are verified through the immunomic network.