中文摘要：

利用矩阵的半张量积，通过建立逻辑变量与向量的对应，块序列布尔网络被表示为离散时间系统，将对序列布尔网络的研究转化为对结构矩阵的研究．块序列布尔网络的结构矩阵是一个逻辑矩阵，利用逻辑矩阵的1特征值与和1特征向量的特殊性质，从矩阵特征值和特征向量的角度研究了块序列布尔网络的拓扑结构，显式表示出了不同长度极限环的个数，并指出网络的极限环总数等于（2^n-结构矩阵的秩）．

英文摘要：

Topological properties of block sequential Boolean networks are discussed by means of matrix theory. Using semi-tensor product, we express logical variables in vector forms and thus the block sequential Boolean network is ex- pressed in a discrete time system. Based on the 1 eigenvalue and the 1 eigenvectors of the structure matrix, the numbers of limit cycles with different lengths are expressed in explicit formulas. Especially, the total number of all cycles is obtained as （（2^n - r）, where r is the rank of the structure matrix.