Attractor Stabilizability of Boolean Networks With Application to Biomolecular Regulatory Networks

Stabilizability of Boolean networks (BNs) has been addressed in some recent research works. One of the most widespread applications of BNs is the analysis and control of biomolecular regulatory networks. Pertinent to this field of application, we introduce the concept of attractor stabilizability of a BN by flipping a subset of its nodes. This concept captures the possibility of enforcing a BN to converge from any of its attractors to a desired stable state by flipping members of a subset of network variables just once. Our approach is based on the algebraic state-space representation of BNs using semi-tensor product of matrices. In this work, after introducing some new matrix tools, we use them to construct a characteristic matrix called attractor stabilizability matrix. Then, this matrix is used to derive necessary and sufficient conditions for attractor stabilizability of a BN. Two algorithms are then proposed to identify the stabilizing kernel for the target attractor of a BN. The developed approach is successfully applied to several BN models of real biomolecular regulatory networks.