This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on...This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on which and the algebraic form of Boolean networks,a kind of observabihty matrix is constructed.Second,by the observability matrix,a new necessary and sufficient condition is given for the observability of Boolean networks.Third,the concept of observabihty index for observable Boolean networks is defined,and an algorithm is established to calculate the observability index.Finally,a practical example of D.Melanogaster segmentation polarity gene networks is studied to support our new results.The study of the illustrative example shows that the new results obtained in this paper are very effective in investigating the observability of free Boolean networks.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.61034007,61174036,and 61374065the Research Fund for the Taishan Scholar Project of Shandong Province of China
文摘This paper investigates the observabihty of free Boolean networks by using the semi-tensor product method,and presents some new results.First,the concept of observability for free Boolean networks is proposed,based on which and the algebraic form of Boolean networks,a kind of observabihty matrix is constructed.Second,by the observability matrix,a new necessary and sufficient condition is given for the observability of Boolean networks.Third,the concept of observabihty index for observable Boolean networks is defined,and an algorithm is established to calculate the observability index.Finally,a practical example of D.Melanogaster segmentation polarity gene networks is studied to support our new results.The study of the illustrative example shows that the new results obtained in this paper are very effective in investigating the observability of free Boolean networks.
