This paper investigates the global attractive set of neural networks with neutral item. To better deal with the neutral terms, different types of activation functions are considered. Based on matrix measures, inequality techniques, and Lyapunov theory, three new types of Lyapunov functions are designed to find the global attractive set of the system. We give out a simulation example to verify the validity of theory results. The result is very inclusive, whether the system has equilibrium or not. As long as the system is stable, we can find its global attractive set
