This article aims to deal with the effects of short-term depression (STD) in a excitatory and inhibitory neuronal network rate models. A conclusion is known that increasing STD leads to an increase of the length of high activity state together with a vanishing of the low state[1] via a complex process. Due to the complexity of that model, I plan to establish a simple model which could cope the same result of STD effect. Thus, depended on Hodgkin-Huxley model and population rate model, the effect could be represented by three kinds of variables which are synaptic activities, undepression variable and cellular adaptation, where synaptic depression and cellular adaptation variables are so-called slow variables. In order to reproduce the experimental result, I simulate parameter values by C program to find the presence of bifurcation which is mentioned with that result. . It has been described, in computational tests of large biophysical networks, that the increase of short-term synaptic depression leads to a bifurcation from oscillatory to asynchronous behaviour. However, the phenomenon may be accounted for with simpler minimal models. The project consists of explaining this bifurcation by means of a set of 6 ODEs (describing population rate, a negative subtractive feedback and a divisive feedback, both in the excitatory and inhibitory poulations). Modelling, computational and analytical tools (dynamical systems) will be required