Abstract
Abstract The study of logical matrix factorization provides a new insight into the matrix dimension reduction problems of biological systems. This paper develops the logical matrix factorization technique for exploring the topological structure and stability of probabilistic Boolean networks (PBNs). Firstly, the union set of distinct indices in factorized structural matrices for different modes is obtained, based on which, a size-reduced system is constructed for the original PBN. Secondly, it is proved that the topological structure of original PBN is equivalent to that of the size-reduced system. Thirdly, the equivalence of finite-time stability and stability in distribution between the original PBN and the size-reduced system is further revealed. Finally, the effectiveness of the obtained new results are verified via several Boolean models of genetic regulatory networks (GRNs).
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