# Pars a fluctuating parameter in an ODE

**URL:** https://discourse.julialang.org/t/pars-a-fluctuating-parameter-in-an-ode/42134
**Category:** New to Julia
**Tags:** ode
**Created:** [June 26, 2020, 10:12pm UTC](https://discourse.julialang.org/t/pars-a-fluctuating-parameter-in-an-ode/42134 "2020-06-26T22:12:07Z")
**Posts on this page:** 5
**Page:** 1

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### Author: ![99dB](https://avatars.discourse-cdn.com/v4/letter/9/838e76/32.png) [@99dB](https://discourse.julialang.org/u/99dB)
#### Post date: [June 26, 2020, 10:12pm UTC](https://discourse.julialang.org/t/pars-a-fluctuating-parameter-in-an-ode/42134/1 "2020-06-26T22:12:07Z")

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Dear Julia users,

I am new to julia and I want to solve an ODE system with some fluctuating parameters.  
Let say that I have a fluctuating temperature T as function of time:

```julia
T = 18
time = collect(0:0.01:365)
vecT = T.+0.2*T*sin.((1/10)*2*pi.*time);
fig, ax=PyPlot.subplots(figsize=(8,2))
ax.plot(vecT)

```

 ![Test_T](https://global.discourse-cdn.com/julialang/original/3X/d/3/d33e29ddaa7e582153f83b56be9fb715f686595f.png)

Let say I have a parameter that is a funciton of T in my ODE. How can I implement it?

```julia
# The ode model
function dudt(u,p,t)  
    a = p[1];
    b = p[2];
    μ = a*exp(-b/T(t))
    ψ = p[3];
  
    return μ-ψ  
end

```

Many thanks for your help

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<div class="post-metadata">

### Author: ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [June 26, 2020, 10:56pm UTC](https://discourse.julialang.org/t/pars-a-fluctuating-parameter-in-an-ode/42134/2 "2020-06-26T22:56:01Z")

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Just define `f(t) = T.+0.2*T*sin.((1/10)*2*pi.*t)` and then use it inside of your ODE

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### Author: ![99dB](https://avatars.discourse-cdn.com/v4/letter/9/838e76/32.png) [@99dB](https://discourse.julialang.org/u/99dB)
#### Post date: [June 26, 2020, 11:02pm UTC](https://discourse.julialang.org/t/pars-a-fluctuating-parameter-in-an-ode/42134/3 "2020-06-26T23:02:55Z")

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Thanks a lot @ChrisRackauckas ChrisRack.  
I have an additional question, if my temperature is not a function but a vector of data. Is there is a way do take the T(t) in the ode function?

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<div class="post-metadata">

### Author: ![ChrisRackauckas](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/chrisrackauckas/32/77_2.png) [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [June 26, 2020, 11:09pm UTC](https://discourse.julialang.org/t/pars-a-fluctuating-parameter-in-an-ode/42134/4 "2020-06-26T23:09:33Z")

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> **[GitHub - SciML/DataInterpolations.jl: A library of data interpolation and...](https://github.com/SciML/DataInterpolations.jl)**
>
> A library of data interpolation and smoothing functions - GitHub - SciML/DataInterpolations.jl: A library of data interpolation and smoothing functions

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<div class="post-metadata">

### Author: ![99dB](https://avatars.discourse-cdn.com/v4/letter/9/838e76/32.png) [@99dB](https://discourse.julialang.org/u/99dB)
#### Post date: [June 26, 2020, 11:17pm UTC](https://discourse.julialang.org/t/pars-a-fluctuating-parameter-in-an-ode/42134/5 "2020-06-26T23:17:15Z")

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Thanks!