Synchronization of Interconnected Boolean Networks with Stochastic Function Perturbations

Abstract

In this paper, synchronization of interconnected Boolean networks subject to stochastic function perturbations is investigated by resorting to the semi-tensor product technique. First, the concept of stochastic function perturbations for interconnected Boolean networks is introduced base on the algebraic state space representation. Then, by constructing a transition probability matrix, a necessary and sufficient condition is obtained assuring the synchronization of the interconnected Boolean networks under stochastic function perturbations. Subsequently, the synchronization of interconnected Boolean networks with positive probability is further studied, and an algebraic synchronization criterion is established. Finally, a numerical example is employed to illustrate the efficiency of the obtained theoretical results.