RateSystem

[raphael-roemer]

We would like to add functionality for Rate dependent forcing functionality and easy system creation of non-autonomous systems

[reykboerner]

Thanks a lot for working on this!

I very much like the idea of starting with the general mathematical formulation \dot x = f(x(t), lambda(t)), and have made a suggestion of how this could be reflected more in the way a user would define a RateSystem.

One thing I am unsure about is whether we just need a constructor function RateSystem that returns either a CoupledODEs or CoupledSDEs, or whether we need an additional type in order to pass the necessary information about the rate system to the methods we want to add.

Maybe we can brainstorm the methods we would like to add here and think about whether they work with a CoupledODEs or whether we need more.

[reykboerner]

It should be sufficient to use DynamicalSystemsBase.

[reykboerner]

In my opinion, these are quite many positional arguments, which makes it less user-friendly. What do you think of reorganising this in the following structure:

RateSystem(ds::ContinuousTimeDynamicalSystem, rate_protocol::function)

where ds can be a CoupledODEs or a CoupledSDEs and rate_protocol is your λ function that determines how the parameters change over time. This function could have the structure

rate_protocol(u, p_lambda, t; t_start=0.0, t_end=Inf, kwargs...)

i.e. it would contain all the input arguments needed to define the rate forcing function. Behind the scenes, this would then create and return a new CoupledODEs or CoupledSDEs with the explicit time dependence specified by rate_protocol.

[reykboerner]

The naming here is just a suggestion, but generally I think we should give more descriptive names than just lambda or tnf (clarity over brevity!)

[raphael-roemer]

This sounds great, thanks Reyk! However, rate_protocol should not depend on u, in my opinion.