Stability of Boolean Networks With Delays Using Pinning Control

Abstract

This paper investigates pinning control for stabilizing Boolean networks with time delays. The purpose of this paper is to design a control algorithm to select a fraction of key nodes for a Boolean network with time delays such that the considered Boolean network can achieve stability. First, by changing the columns of the transition matrix of a Boolean network, the stabilization of a Boolean network is investigated. By doing this, we can obtain a new transition matrix for which we can select the key nodes. Furthermore, an algorithm is then proposed to design a pinning controller. Finally, an example of pinning control of coupled oscillators in the cell cycle is presented to show the effectiveness of the proposed results.