A New Approach to Pinning Control of Boolean Networks

Boolean networks (BNs) are discrete-time systems where nodes are inter-connected (here we call such connection rule among nodes as network structure), and the dynamics of each gene node is determined by logical functions. In this paper, we propose a new approach on pinning control design for global stabilization of BNs based on BNs' network structure, named as network-structure-based distributed pinning control. By deleting the minimum number of edges, the network structure becomes acyclic. Then, an efficient distributed pinning control is designed to achieve global stabilization. Compared with existing literature, the design of pinning control is not based on the state transition matrix of BNs. Hence, the computational complexity in this paper is reduced from $O(2^n\times 2^n)$ to $O(2\times 2^K)$, where $n$ is the number of nodes and $K\leq n$ is the largest number of in-neighbors of nodes. In addition, without using state transition matrix, global state information is no longer needed, the design of pinning control is just based on neighbors' local information, which is easier to be implemented. The proposed method is well demonstrated by several biological networks with different sizes. The results are shown to be simple and concise, while the traditional pinning control can not be applied for BNs with such a large dimension.