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JuliaDynamics / Attractors.jl

Find attractors of dynamical systems, their basins, and continue them across parameters. Study global stability (a.k.a. non-local, or resilience). Also tipping points functionality.
MIT License
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Finish tutorial and matcher interface #134

Closed Datseris closed 5 days ago

Datseris commented 6 days ago

This PR finishes the tutorial and also truly finishes the matcher interface. The interface is based on the matching_map function, which is a rename of the replacement_map function. See the docstring of IDMatcher and matching_map for the new interface.

The PR adds a comparison also with BifurcationKit.jl.

In this PR I've also implemented the desired MatchByBasinEnclosure. It is part of the interface now so it is exported and added to the docs. I've also tested that it "runs" with the tutorial example. But, I have no good system at the moment to test it with. If I use the system of the tutorial, and after I match the normal way with the tutorial I try again by doing:

matcher = MatchByBasinEnclosure()
attractors_cont2 = deepcopy(attractors_cont)
match_sequentially!(attractors_cont2, matcher; ds, prange, pidx)
fig = plot_attractors_curves(
    attractors_cont2, A -> minimum(A[:, 1]), prange,
)

then I get

image

notice how when we go into the first bistable regime there is something wonky (a black triangle is high in y axis), and when we go to the second bistable regime the attractor labels alternate all the time. I don't know if this is correct for this system because the basins are super duper fractal and thus everything all the time fluctuates a lot, or there is something wrong in my logic. In any case, I'd appreciate some help testing this new matcher.

Datseris commented 5 days ago

I am presenting this tomorrow so I am merging it in. It would be fantastic to get tests for the new basin enclosure matcher @KalelR , but this can be done when you have some time. Would also be fantastic to have an Example with your kuramoto system that shows that using other matchers doesn't work as well.