I wrote down my understanding of Doelling etal's (PNAS 2019) description of their Wilson-Cowan oscillator model. Happy to learn what I did wrong -- please let me know :)!
implements the model as specified by Doelling etal (or at least as I understand it!).
calls myWilsonCowan with the driving force set to 0 to check if it indeed has a 4 Hz resting activity. Doelling et al describe that for the parameters they chose, this should be the case.
As we see in the figure above, this seems to be the case.
runs a simple periodic input with some decay into the oscillator model and a barbarically simple evoked model. I am checking if I can reproduce their figure 1 intuition (i.e. a variable phase difference between stimulus and response for constant lag LTI model and a constant phase difference with a variable time lag for the oscillator model).
I would have liked to see the filtered responses in the figure by Doelling etal!
As far as I can see in the figure above, in this simple setup, everything seems to work more or less as expected.
runs more frequencies at different intensities into the evoked and oscillator model (calling runEvOsc.m which is a quick and dirty function copy-pasted from doellingIntuition.m). I didn't find any information on how Doelling et al set the intensity of their input, i.e., whether they normalised and/or rescaled their input, and was wondering if the output depends on the input intensity.
We see here the phase differences (stimulus vs response) for evoked (left) and oscillatory responses (right).
As expected, the evoked responses show a variable phase difference across frequencies, and we see they aren't much impressed by the intensities.
We then also see that the oscillatory model has a more or less constant phase difference (as described by Doelling et al) across frequencies for intensities around 1 --3. For other intensities however, the angle is more variable.
I guess the point is that this model has the potential to have a stable phase difference.