[WIP] nonlocal stability measure estimator

[Datseris]

This PR is by @andreasmorr and adds a nonlocal stability estimator construct that can compute every nonlocal stability measure at once during finding attractors and/or during the continuation.

[Datseris]

All these dictionaries should state StateSpaceSet{D, T} and {D, T} should be type parameters of the struct.

[andreasmorr]

What's the cleanest way to extract the specific {D, T} from a given mapper?

[Datseris]

D = dimension(ds)
T = eltype(current_state(ds))

[Datseris]

I think this is special. Measures that require parameter change do not fit to this interface. We need to create another function for them I think...

[andreasmorr]

Yes I agree. Can we still include it in this PR/ file though?

[Datseris]

Sure, if you want to, but it has to be a separate function for source code clarity. It would be a function you run after global_continuation has finished and you utilize the attractors_cont output.

[Datseris]

plotting is simple, we don't need a specialized function:

attractors_cont, all_measures = global_cont(stability_accumulator)

all_measures = vector ( dictonary ( measure_name => dictionary (id => number) ) )

mcs = [dicts["minimal_fatal_shock_magnitude"] for dicts in all_measures]

plot_continuation_curves(mcs, parameter_curve)

[Datseris]

I just found the paper: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.93.042205 "Constrained basin stability for studying transient phenomena in dynamical systems".

It is identical to estimating the basin stability, but instead of weighting the distribution by a given density ρ, you weight the distribution by a "selector function". Only trajectories whose transients satisfy property "X" are counted. I think it is very straightforward to add this as yet another indicator in this PR.

We make a function indicator(u0, ds, tc) with ds the dynamical system. Inside this function the user may perform arbitrary numerics of whether the trajectory starting from u0, with arbitrary transient, satisfies the condition. tc is the convergence time that we have already estimated from the given initial condition at the previous step of the aglroithm of estimating all other stability measures. then the indicator function returns true/false, which tells whether to add u0 to the count or not.

@andreasmorr I can add this functionality in the code once the PR is ready to go.