7.1  Regarding the Mathematical Definition of SD

To implement synaptic depression in our model, we introduced an adaptation variable A to our model, governed by equations 3.2 to 3.4. These equations represent synaptic depression as a convolution with an alpha kernel with rate α and timescale τA. We solved the convolution integral to express it as a set of differential equations (see equations 3.5 and 3.6). However, equation 3.6 contains an erroneous scaling of the input firing rate r with the capitation time constant τA. The convolution integral in equation 3.2 can be expressed as a second-order differential equation:
The equation can be transformed into a set of two coupled first-order differential equations under a simple change of variables:
Equation 7.3 differs from equation 3.6 merely by a constant scaling of r with τA. Since we have never varied τA in this study, this has no impact on our results. Still, the reported values of α for which we find synchronized bursting hold only for synaptic depression given by equations 7.2 and 7.3.