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Bifurcation-theoretic origin of RPO8

Determine the bifurcation-theoretic origin of the relative periodic orbit RPO8 in vertical thermal convection in the [1,8,9] domain with Pr=0.71, including identifying the invariant solution or bifurcation mechanism from which RPO8 emerges.

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Background

RPO8 lies in the symmetry subspace generated by a two-fold diagonal translation and undergoes multiple saddle-node bifurcations over the studied Rayleigh number range.

Despite continuation, the authors could not trace RPO8 back to a known bifurcating source.

References

With the available information, we have not been able to determine the origin of RPO8.

— 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 4.4.2 (RPO8: saddle-node bifurcations)