Feature: Higher-order Bautin normal form and unfolding#254
Feature: Higher-order Bautin normal form and unfolding#254mmbosschaert wants to merge 6 commits into
Conversation
This test validates the higher-order Bautin normal form computation and predictor: - Uses Symbolics.jl to compute jet derivatives up to 7th order - Tests Stuart-Landau equation with quintic and septic nonlinearities - Verifies l2 and l3 coefficients match theoretical formulas (4·c5 and 8·c7) - Confirms predictor actually uses c₃ (l3) by comparing predictions with/without it - Shows parameter predictions differ by ~1e-7 when c₃ is included vs zeroed The test proves the higher-order predictor is working correctly.
|
Thanks a lot for this massive PR! I will review this asap. Best regards |
| ~cv && @debug "[Bautin H3100] Linear solver for J did not converge. it = $it" | ||
|
|
||
| h2200 = D40(q0, q0, cq0, cq0) .+ | ||
| 4 .* C(q0, cq0, H1100) .+ C(cq0, cq0, H2000) .+ C(q0, q0, conj.(H2000)) .+ |
|
|
||
| G32 = dot(p0, D50(q0, q0, q0, cq0, cq0)) | ||
| G32 += (dot(p0, D40(q0, q0, q0, conj.(H2000))) + | ||
| 3dot(p0, D40(q0, cq0, cq0, H2000)) + |
|
You should modify the documentation as well You can probably add your name and a link to this PR there to underline you contribution |
|
It seems your code only works for 2d systems as I have tried locally. I suggest minor changes in |
|
If you want some help, I need to be able to push to your PR. This is possible as explained here
|
|
Thanks. It looks like ‘Allow edits and access to secrets by maintainers’ is already checked. Am I missing something? |
|
I am not sure I am a maintener on your branch, am I? |
Resolve conflicts in NormalForms.jl, periodicorbit/NormalForms.jl, Problems.jl, and codim2/NormalForms.jl. Widen _field_jet/_type_jet to include R20..R70 and R41/R51. The higher-order Bautin code reads these jet fields directly and they were outside upstream's constraint. Route a user-supplied R01 function into jet.R01. Upstream made R01 an explicit BifurcationProblem kwarg defaulting to AutoDiff(), which captured user functions before they reached the jet. Only the dispatch when R01 is neither AutoDiff() nor FiniteDifferences() changes. Track upstream renames in the higher-order branch: bare dot to LA.dot, I to LA.I, and alias prob_ma = 𝐌𝐚.
Conflict in src/periodicorbit/PeriodicOrbitCollocation.jl: upstream split po_analytical_jacobian! into a thin wrapper plus inner _collocation_analytical_jacobian! taking the time-slice matrix and period directly, and added an optional _compute_borders. The higher-order Bautin branch never touched this function, so the resolution takes upstream's refactor verbatim.
|
Is there something I can do for the PR to be approved at this stage? |
|
Hi, Have you adressed the comments/review in the code? |
Rotate the padded Stuart-Landau system by an orthogonal Q in the (1,3) plane so the third coordinate is used while l2 and l3 keep their 2D values 4*c5 and 8*c7. The test checks the eigenvector has a non-zero third component to make sure the computation is not restricted to planar systems.
|
I've added an example demonstrating that the normalization method also works in a higher dimensional system. |
|
Hi, have you been able to verify that the predictor works in higher-dimensional systems? If so, is there still work for me to do on the PR before it can be merged? |
|
Hi, I just pushed a few refactor but there is a conflict. Very strange... |
Adapt the higher-order Bautin normal form and its test to the unified codim-2 bifurcation point struct.
|
Hi, It should be fixed now. Please let me know if I can do anything else to help with the merge. |
|
That is strange, I am not sure my changes have been pushed. Actually yes, it is here https://github.com/bifurcationkit/BifurcationKit.jl/blob/bautin-local/test/normal_forms/test_bautin_higherorder.jl But it does not appear in the commits of this PR. |
I need to read your code in detail. |
|
I think there is a big issue: julia> 1 +
1
2BUT julia> 1
+1
1this is used everywhere in your implementation |
|
Note that every multi-line sum is wrapped in parentheses, e.g., h4300 = ( ... ), and inside parentheses, Julia does continue across newlines, so no terms are dropped: julia> ( 1 The higher-order test relies on this: l3 is computed from h4300 (the largest of these formulas) and The leading-operator style is fragile since it leans on the parentheses, so happy to move the operators |
good catch |
2 participants
Higher-Order Bautin Normal Form and Unfolding
This PR implements higher-order computation of the Bautin (Generalized Hopf) normal form and its associated predictor for fold of periodic orbits continuation.
Summary
The Bautin bifurcation occurs when the first Lyapunov coefficient vanishes at a Hopf point, requiring higher-order analysis. Previously, the code computed up to the second Lyapunov coefficient. This PR extends the computation to the third Lyapunov coefficient and implements a higher-order predictor that uses additional higher-order parameter-dependent terms for more accurate approximation to the fold of period orbits curve emanating from the Bautin bifurcation point.