Control gain and cost of pinning control for BA scale-free networks

This paper investigates the pinning control strategy of BA scale-free network through numerical analysis. A new cost function is defined to measure the cost of pinning control. Compared with the control gain and the cost of pinning nodes with smallest degree or biggest degree, an interesting result is that a smaller control gain and a lower cost are achieved by using the control scheme of pinning nodes with smallest degree. Moreover, there is a minimal control cost by pinning nodes with smallest degree and biggest degree, respectively. The number of controllers by pinning nodes with smallest degree is considered finally.