`ODESystem` not dealing with dynamic parameters

[Sush1090]

Describe the bug 🐞
Hello the question was first posted here

I have repeated it below.

ODE solver does not consider the parameter to be dynamic. Instead fixes the value to be at t=0
Expected behavior

The chosen parameter should change over t and should affect the solution to the ODE.

Minimal Reproducible Example 👇

using ModelingToolkit, DifferentialEquations
using ModelingToolkit: t_nounits as t, D_nounits as D

function test(;name)
    vars = @variables begin
        x(t)
    end
    para = @parameters begin
        α(t)
    end
    eqs = [
        D(x) ~ α
    ]
    ODESystem(eqs,t,vars,para,name=name)
end
@named model = test()
sys = structural_simplify(model)
para = [sys.α => cos(t)]
u0 = [sys.x => 1]
tspan = (0,2π)
prob = ODEProblem(sys,u0,tspan,para)
sol = solve(prob)

Error & Stacktrace ⚠️
No error

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

[961ee093] ModelingToolkit v9.62.0
[0c46a032] DifferentialEquations v7.15.0

• Output of using Pkg; Pkg.status(; mode = PKGMODE_MANIFEST)

• Output of versioninfo()

Julia Version 1.11.3
Commit d63adeda50 (2025-01-21 19:42 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 20 × 12th Gen Intel(R) Core(TM) i7-12800H
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 1 default, 0 interactive, 1 GC (on 20 virtual cores)

Additional context

[tpdsantos]

Dynamic parameters work differently from variables. In order to do that, you need to create a callable parameter of the form (param ::FuncType)(..) and then call param(t) inside the equations:

using ModelingToolkit, DifferentialEquations
using ModelingToolkit: t_nounits as t, D_nounits as D

function test(;name)
    vars = @variables begin
        x(t)
    end
    para = @parameters begin
        (α ::Function)(..)
    end
    eqs = [
        D(x) ~ α(t)
    ]
    ODESystem(eqs,t,vars,para,name=name)
end
@named model = test()
sys = structural_simplify(model)
para = [sys.α => cos] # the input must be the function
u0 = [sys.x => 1]
tspan = (0,2π)
prob = ODEProblem(sys,u0,tspan,para)
sol = solve(prob)

For more information, you can go to the documentation page about callable parameters: https://docs.sciml.ai/ModelingToolkit/stable/tutorials/callable_params/#Callable-parameter-syntax