Dice Question Streamline Icon: https://streamlinehq.com

Termination of RPO20 branch at its other endpoint

Determine how the relative periodic orbit RPO20 terminates at its other endpoint under Rayleigh-number continuation, identifying the bifurcation type or invariant state encountered.

Information Square Streamline Icon: https://streamlinehq.com

Background

RPO20 exists in a narrow Rayleigh number interval and appears to bifurcate from FP4 via a global homoclinic bifurcation where its period increases markedly.

The nature of the termination at its other endpoint remains unresolved.

References

The termination of the other end of the RPO20 branch is unclear and not discussed.

— 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 4.3.2 (RPO20: saddle-node and global bifurcations)