Necessary and sufficient criterion for node synchronization in impulsive Boolean networks

Boolean networks (BNs) are discrete-time dynamical systems with Boolean state-variables. Recently, BNs are widely used to model genetic regulatory networks and biological systems. In this paper, we consider the synchronization of coupled nodes in Boolean networks with impulsive effects. Necessary and sufficient synchronization criterion for coupled nodes in Boolean networks with impulsive effects are presented by converting the logical system into algebraic expression. Our results are based on the approach of semi-tensor product of matrices. Some convenient criteria are proposed to judge whether Boolean network with impulses can be synchronized. Finally, one illustrative example is given to show the validness of our proposed results.