Necessary and sufficient conditions for asymptotic synchronization of drive-response coupled stochastic Boolean networks

Abstract

This paper studies the asymptotic synchronization of drive-response stochastic Boolean networks. We propose two coupled Boolean networks with stochastic sequences and then derive their algebraic forms using semi-tensor product property. Subsequently, a novel eigenvalue-based approach is introduced to establish necessary and sufficient conditions for the asymptotic synchronization of these networks. While prior synchronization results were typically derived from the powers of the transition probability matrix, our method requires only the eigenvalues of this matrix. Finally, several examples are provided to validate the results obtained.