Hello,
I am interested in solving Wilson - Cowan equations (or in general, a differential equation where noise is not multiplicative or additive per se, but put inside an activation function). For example:
\frac{dx}{dt} = f(x(t) + \xi(t))
f(x) = \frac{1}{1+e^{-x}}
The “noise inside a nonlinar function” phenomenon is very common in the literature of large-scale brain modeling in computational neuroscience literature (Wilson Cowan model, Wong-Wang model, Chaudhuri model etc., to name a few).
It seems from the documentation that noise can be either additive or multiplicative, but can’t be inside a nonlinear function. Is there a way to implement this with DifferentialEquations.jl or would I have to write custom code to handle this.
Thanks for the great work,
Yasir