This paper presents a modified astrocyte model that allows a convenient digital implementation. This model is aimed at reproducing relevant biological astrocyte behaviors, which provide appropriate feedback control in regulating neuronal activities in the central nervous system. Accordingly, we investigate the feasibility of a digital implementation for a single astrocyte and a biological neuronal network model constructed by connecting two limit-cycle Hopf oscillators to an implementation of the proposed astrocyte model using oscillator-astrocyte interactions with weak coupling. Hardware synthesis, physical implementation on field-programmable gate array, and theoretical analysis confirm that the proposed astrocyte model, with considerably low hardware overhead, can mimic biological astrocyte model behaviors, resulting in desynchronization of the two coupled limit-cycle oscillators.