Support for continuation of user-defined event manifolds in codim-2 continuation

[MaxwellDemonLin]

Hi,

Currently, codim-2 continuation supports tracking bifurcation curves such as Fold and BP point. I was wondering whether it is possible to extend this framework to user-defined events, not just detect them but actually continue them as curves.

I understand that this is probably a rather niche use case, but it would be very useful for problems involving switching conditions, activation boundaries, or other non-standard physically meaningful events.

[rveltz]

I have to think about this...
Do you have an example in mind? Do you have a similar feature in other bifurcation software?

[MaxwellDemonLin]

Hi, thanks for your reply.

In my system, I have a grid-connected inverter with a current limit. As the load increases, the inverter current increases until it reaches this limit. Once the limit is triggered, the system switches to a different model, and I continue the analysis with that system.

What I want to study is the following:

The load is one parameter
The current limit is another parameter

For each value of the current limit, there is a triggering point along the load continuation where the limit is reached.

I would like to track how this triggering point moves as the current limit changes, i.e., obtain a curve in the two-parameter space.

From my perspective, this is not a standard bifurcation, it is a discontinue bifurcation point in a piecewise-smooth system, because at this point jacobian have changed.

The problem can be defined as follows: I have a system boundary point defined by an event, and this switching process causes discontinuous bifurcation. I want to trace this point.

[rveltz]

We might need an API for this but you can do it yourself, it will take less time.

function follow_point(u, p)
    p2 = u[end]
    newp = @set p.myoptic_for_p2 = p2
    res = my_residual(u[1:end-1], newp)

    p1 = p.p1 # or whatever optic
    return vcat(res, condition(p1, p2))
end

wrap it into a problem

prob = BifurcationProblem(follow_point, [state, pars.p2], pars, @optic _.p1)

and continue it wrt to your parameter p1.

When you have a working example, we can (PR? ) add this to functionality to BifurcationKit

[MaxwellDemonLin]

Hi,

Thank you for your help.

This method works for me.

[rveltz]

Great