Robust cluster synchronization of Boolean networks with function perturbation

Abstract

This paper analyzes the cluster synchronization of Boolean networks (BNs) subject to deterministic function perturbation. Firstly, the perturbation injection matrix is constructed based on the structure matrix of original BNs and the information of function perturbation to determine whether the cluster synchronization is still maintained after one-bit function perturbation occurs. Secondly, based on the idea of robust cluster synchronization of BNs subject to one-bit function perturbation, we give a necessary and sufficient condition for robust cluster synchronization of BNs with multi-bit function perturbations. Finally, as an application, the robust feedback cluster synchronization is further studied for Boolean control networks subject to function perturbation.