# Noise inside an activation function in DifferentialEquations.jl

**URL:** https://discourse.julialang.org/t/noise-inside-an-activation-function-in-differentialequations-jl/118219
**Category:** Modelling & Simulations
**Tags:** random, differentialequation
**Created:** [August 15, 2024, 10:40am UTC](https://discourse.julialang.org/t/noise-inside-an-activation-function-in-differentialequations-jl/118219 "2024-08-15T10:40:21Z")
**Posts on this page:** 3
**Page:** 1

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### Author: ![duodenum](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/duodenum/32/36258_2.png) [@duodenum](https://discourse.julialang.org/u/duodenum)
#### Post date: [August 15, 2024, 10:40am UTC](https://discourse.julialang.org/t/noise-inside-an-activation-function-in-differentialequations-jl/118219/1 "2024-08-15T10:40:21Z")

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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

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### Author: ![isaacsas](https://avatars.discourse-cdn.com/v4/letter/i/f6c823/32.png) [@isaacsas](https://discourse.julialang.org/u/isaacsas)
#### Post date: [August 15, 2024, 6:34pm UTC](https://discourse.julialang.org/t/noise-inside-an-activation-function-in-differentialequations-jl/118219/2 "2024-08-15T18:34:32Z")

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Seems like this is a random ODE: [Random Ordinary Differential Equations · DifferentialEquations.jl](https://docs.sciml.ai/DiffEqDocs/stable/tutorials/rode_example/)

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### Author: ![duodenum](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/duodenum/32/36258_2.png) [@duodenum](https://discourse.julialang.org/u/duodenum)
#### Post date: [August 18, 2024, 3:19am UTC](https://discourse.julialang.org/t/noise-inside-an-activation-function-in-differentialequations-jl/118219/3 "2024-08-18T03:19:13Z")

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thanks!