#55 Continuation of a P2-orbit in an non-autonomous ODE: How to deal with the gluing conditions

[Alois Steindl]

Dear Harry and colleagues,
when trying to introduce my students to coco, I encountered a problem with the preparation of the continuation of a P2-orbit:
I am looking at a Mathieu-like oscillation equation

x'' + x + gamma x' + beta x^3 + delta x^2 x' = a sin(2*pi/per*T)

In the first run I start with the trivial (periodic) solution and find several BPCs and PD points when varying the excitation period per.
Then I would like to look at the periodic solutions starting at the PD points. Here I have difficulties in specifying the proper gluing conditions between the obtained orbit period T and the parameter per; T should be 2 per. When I use the command

prob = coco_add_glue(prob, 'glue', uidx(maps.T_idx), uidx(maps.p_idx(5)));

I get an error message, that no solution could be found.
If I leave this command out, I obtain new branches, but these vary the period T and leave per fixed.

So how would I tell coco, that the gluing condition should be T=2 per?
(I could imagine to introduce a global variable, which takes care of the multiplicity. Or I could convert the problem to an autonomous one. What would you suggest as good solution?
With kind regards
Alois

[Alois Steindl]

Sorry, I missed to attach the input file in the first post. Here it comes.
With kind wishes
Alois

[Harry Dankowicz]

Please see the responses in ticket #51.

Kind regards,

Harry