The stability of Boolean networks has attracted much attention due to itswide applications in describing the dynamics of biological systems. During thepast decades, much effort has been invested in unveiling how network structureand update rules will affect the stability of Boolean networks. In this paper,we aim to identify and control a minimal set of influential nodes that iscapable of stabilizing an unstable Boolean network. By minimizing the largesteigenvalue of a modified non-backtracking matrix, we propose a method using thecollective influence theory to identify the influential nodes in Booleannetworks with high computational efficiency. We test the performance ofcollective influence on four different networks. Results show that thecollective influence algorithm can stabilize each network with a smaller set ofnodes than other heuristic algorithms. Our work provides a new insight into themechanism that determines the stability of Boolean networks, which may findapplications in identifying the virulence genes that lead to serious disease.
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