A New Approach to Pinning Control of Boolean Networks

Boolean networks (BNs) are discrete-time systems, where nodes are interconnected (here, we call such connection rule among nodes as a network structure), and the dynamics of each gene node is determined by logical functions. In this article, 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. Compared with the existing literature, the design of pinning control is not based on the state transition matrix of BNs. Hence, the computational complexity in this article is reduced from
$O(2^{2n})$
to
$O(n^2+n2^K)$
, where
$n$
is the number of nodes and
$K\leq n$
is the largest number of in-neighbors of nodes. In addition, without using the 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 implement. 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 cannot be applied for BNs with such a large dimension.