The local convergence of Boolean networks with disturbances

his paper is devoted to studying the local convergence of Boolean networks (BNs) with disturbances. On the one hand, the algebraic form of a BN with n nodes and n disturbances is obtained by semi-tensor product (STP) of matrices, and based on the algebraic expression, some conditions of the local convergence are presented. On the other hand, by the discrete derivative of Boolean functions at a fixed point, a new matrix with dimension nxn(not 2nx2n)is constructed to analyze the local convergence, and it implies that the computational complexity is dramatically reduced from O(2(2n)) to O(n(2))compared with the method of STP. Finally, examples are provided to illustrate the effectiveness of the obtained results.