Function perturbations in Boolean networks with its application in a D. melanogaster gene network

This paper considers the impacts on attractors of function perturbations in Boolean networks via semi-tensor product of matrices. Two types of function perturbations: one-bit perturbation and modifications of update schedule, are investigated. First, the algebraic form of perturbed Boolean networks under one-bit perturbation is given, based on which several necessary and sufficient conditions of different kinds of effects on state transition and attractors are obtained. Besides, a Boolean network with update schedule is studied and the definition of its adjacent diagraph is first presented in this paper. Furthermore, transition matrix of the updated network is calculated to analyze the changes of fixed points and limit cycles. At last, identifying function perturbations with its application in a Drosophila melanogaster segmentation polarity gene network is shown to demonstrate the practicability and effectiveness of the theoretical results.