Uniformly partial stability of Boolean network

The paper deal with problems on stability of Boolean networks with respect to a given part of variables characterizing the Boolean network. Using semi-tensor product of matrices and the matrix expression of logic, the dynamics of a Boolean network can be converted to a discrete time linear dynamics, called the algebraic form of the Boolean network. Main results consist of two parts: (i) From the algebraic form of Boolean network, global partial stability is introduced. (ii) Based on algebraic form, necessary and sufficient condition for global partial states stability with respect to arbitrary initial states are obtained.