Partial stability of probabilistic Boolean network

In this paper, the uniform stability in one part of the variables for probabilistic Boolean networks is discussed. Firstly, definition of partial stability of probabilistic Boolean networks is introduced. Using semi-tensor product, the probabilistic Boolean network is converted to its algebraic form. From the algebraic form of probabilistic Boolean network, necessary conditions are obtained from the structure matrix of probabilistic Boolean network and the condition is based on reachability matrix of probabilistic Boolean network. Hence the necessary condition is straightforward verifiable. At last, a numerical example is provided to demonstrate the corresponding results.