# Is it possible to simulate SDDE with modeling toolkit?
**URL:** https://discourse.julialang.org/t/is-it-possible-to-simulate-sdde-with-modeling-toolkit/125420
**Category:** Modelling & Simulations
**Tags:** modelingtoolkit
**Created:** [January 31, 2025, 8:09am UTC](https://discourse.julialang.org/t/is-it-possible-to-simulate-sdde-with-modeling-toolkit/125420 "2025-01-31T08:09:50Z")
**Posts on this page:** 4
**Page:** 1
### Author:  [@NinaOmejc](https://discourse.julialang.org/u/NinaOmejc)
#### Post date: [January 31, 2025, 8:09am UTC](https://discourse.julialang.org/t/is-it-possible-to-simulate-sdde-with-modeling-toolkit/125420/1 "2025-01-31T08:09:50Z")
Hi,
I’ve come across Chris Rackauckas post that it is possible to simulate DDEs using Modeling Toolkit ([ModelingToolkit: (Transport) delay? Example: Inflow to one water reservoir is a delayed outflow from another - #7 by filip.cerny](https://discourse.julialang.org/t/modelingtoolkit-transport-delay-example-inflow-to-one-water-reservoir-is-a-delayed-outflow-from-another/122654/7)).
Then I tried to simulate SDDE, and it worked, but the solution looked different from the solution when directly using the DifferentialEquations module. Have I made some mistake or is SDDEProblem not yet compatible with ModelingToolkit?
Thank you! I have attached the simplified code below.
Simulating with MTK:
```julia
using DifferentialEquations
using StochasticDelayDiffEq
using ModelingToolkit
using ModelingToolkit: t_nounits as t, D_nounits as D
using Random
using Plots
Random.seed!(1)
@parameters a b τ
@variables x₁(t) x₂(..)
@brownian w₁
eqs = [D(x₁) ~ a * x₁ - x₁ * x₂(t-τ) + 0.2*w₁,
D(x₂(t)) ~ b * x₂(t) + x₁ * x₂(t)]
# Parameters and setup
params = [a => 1., b => -3.0, τ => 0.01]
inits = [x₁ => 1.0, x₂(t) => 1.0]
tspan = (0.0, 20.0)
sys = structural_simplify(System(eqs, t; name=Symbol("LotkaVolterra")))
prob = SDDEProblem(sys, inits, tspan, params; constant_lags=[τ])
sol = solve(prob, SRIW1())
plot(sol, xlims=(0, 20), ylims=(0, 10))
```
Output:
Simulating with differentialEquations:
```julia
using DifferentialEquations
using Plots
using StochasticDelayDiffEq
using StochasticDiffEq
using Random
Random.seed!(1)
function eq!(du, u, h, p, t)
a, b, τ = p
hu2 = h(p, t - τ)[2]
du[1] = a * u[1] - u[1] * hu2
du[2] = b * u[2] + u[1] * u[2] # + h(p, t - τ)[1] # -3 * Vex + Ve * Vex
end
function noise!(du, u, h, p, t)
du1 = 0.2
du2 = 0.
du.= [du1, du2]
end
# Parameters and setup
a, b, τ = 1.0, -3.0, 0.01
params = [a, b, τ]
inits = [1.0, 1.0]
tspan = (0.0, 20.0)
h(p, t) = inits
prob = SDDEProblem(eq!, noise!, inits, h, tspan, params; constant_lags=τ)
sol = solve(prob, SRIW1())
plot(sol, xlims=(0, 20), ylims=(0, 10))
```
Output:
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [January 31, 2025, 9:59am UTC](https://discourse.julialang.org/t/is-it-possible-to-simulate-sdde-with-modeling-toolkit/125420/2 "2025-01-31T09:59:48Z")
@cryptic.ax can you double check the codegen here?
---
### Author:  [@cryptic.ax](https://discourse.julialang.org/u/cryptic.ax)
#### Post date: [January 31, 2025, 11:22am UTC](https://discourse.julialang.org/t/is-it-possible-to-simulate-sdde-with-modeling-toolkit/125420/3 "2025-01-31T11:22:14Z")
Codegen all looks fine. I’ll try and dig further
---
### Author:  [@NinaOmejc](https://discourse.julialang.org/u/NinaOmejc)
#### Post date: [February 6, 2025, 1:31pm UTC](https://discourse.julialang.org/t/is-it-possible-to-simulate-sdde-with-modeling-toolkit/125420/4 "2025-02-06T13:31:24Z")
Thank you for looking into it! I would be happy to know the results of the search.