Comment on terminology: parameter vs. (independent) variable t

[hurak]

Reading the docs for ODESystem, I am somewhat puzzled by the use of the term parameter for time t. In the "hello world" example

using ModelingToolkit

@parameters t σ ρ β
@variables x(t) y(t) z(t)
@derivatives D'~t

eqs = [D(x) ~ σ*(y-x),
       D(y) ~ x*(ρ-z)-y,
       D(z) ~ x*y - β*z]

de = ODESystem(eqs,t,[x,y,z],[σ,ρ,β])

the time t is defined as a parameter (using @parameter), and yet in the documentation for ODESystem(), the second input argument is named as

• iv independent variable.

Do I understand it correctly that we use @parameters for true "physical" parameters (such as σ, ρ, β that do not change during simulation) AND the independent variable (perhaps mostly time t in ODEs), and we use @variables for the dependent variables (functions of the independent variable)?

EDIT: Now I see that the independent variable (time) t is cast as a variable in the section on Derivatives.

@variables t
@derivatives D'~t

This is indeed somewhat confusing. Many thanks for clarification.

[ChrisRackauckas]

t can be a variable. It's just for the automated system definition, i.e. de = ODESystem(eqs), and could possibly be removed since it's one of the archaic things that hasn't really added much value in any recent versions.

[ChrisRackauckas]

using ModelingToolkit

@variables t x(t) y(t) z(t)
@parameters σ ρ β
@derivatives D'~t

eqs = [D(x) ~ σ*(y-x),
       D(y) ~ x*(ρ-z)-y,
       D(z) ~ x*y - β*z]

de = ODESystem(eqs)

Works, so I'll call this a documentation issue. We should probably just move it over as I agree it's a bit confusing.

[ChrisRackauckas]

Just use using ModelingToolkit: t_nounits as t, D_nounits as D