7.1 Regarding the Mathematical Definition of SD
To implement synaptic depression in our model, we introduced an adaptation variable 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 and timescale . 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 with the capitation time constant . 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 with . Since we have never varied in this study, this has no impact on our results. Still, the reported values of for which we find synchronized bursting hold only for synaptic depression given by equations 7.2 and 7.3.
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Massachusetts Institute of Technology