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Bifurcation-theoretic origin of RPO11

Determine the bifurcation-theoretic origin of the relative periodic orbit RPO11 in vertical convection, specifying the invariant solution or bifurcation mechanism that generates RPO11.

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Background

RPO11 has no spatial symmetry and undergoes multiple saddle-node bifurcations; it exhibits roll-breaking and defect dynamics along the orbit.

Continuation to Ra=6680 did not reveal the parent bifurcation or source branch, leaving its origin unknown.

References

We stopped the continuation at $(Ra, T) = (6680, 212)$ for the lower branch and at $(Ra, T) = (6680, 230.6)$ for the upper branch; its origin remains unknown.

— Natural convection in a vertical channel. Part 3. Bifurcations of many (additional) unstable equilibria and periodic orbits (2504.05524 - Zheng et al., 7 Apr 2025) in Section 4.8.2 (RPO11: saddle-node bifurcations)