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Bifurcation-theoretic origin of PO9

Determine the bifurcation-theoretic origin of the periodic orbit PO9 in vertical convection, including identifying the invariant state or bifurcation mechanism from which PO9 emerges.

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Background

PO9 has no spatial symmetry, displays a spatio-temporal symmetry involving reflections and small translations, and undergoes multiple saddle-node bifurcations.

Despite extensive continuation on both branches, the authors were unable to identify the bifurcation mechanism that creates PO9.

References

We have continued the lower branch (in period) of PO9 until $(Ra, T) = (6631.4, 188.7)$ and the upper branch until $(Ra, T) = (6436.72, 323.05)$; the origin of PO9 remains unclear.

— 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 4.8.1 (PO9: saddle-node bifurcations)