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Creation and termination mechanisms for RPO21 and RPO22

Investigate the bifurcation mechanisms that create and terminate the relative periodic orbits RPO21 and RPO22 in vertical convection, clarifying the processes responsible for their appearance and disappearance within the studied parameter range.

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Background

RPO21 and RPO22 belong to a symmetry subspace with five-fold translation and reflection. RPO21 exists only over a short Rayleigh interval without clear endpoints, while RPO22 originates at a saddle-node but its termination is uncertain.

The authors explicitly note unresolved aspects regarding how these orbits are born and/or terminate.

References

Two relative periodic orbits RPO21 and RPO22 are shown in the bifurcation diagram of figure \ref{part3_sepa_BD_PO21_22_23_24}; both undergo a sequence of saddle-node bifurcations, and the termination and/or creation of both orbits remain 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 4.5.2 (RPO21 and RPO22: saddle-node bifurcations)