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

Mechanism behind successive saddle-node bifurcations on RPO29

Explain the mechanism responsible for the large number of successive saddle-node bifurcations observed along the RPO29 branch in the vertical convection system and characterize their origin within the bifurcation structure.

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

Background

RPO29 exhibits at least 13 saddle-node bifurcations before terminating in global homoclinic bifurcations near FP4 and FP2, reminiscent of homoclinic snaking, although no clear spatial localization patterns were found by the authors.

The repeated saddle-node events are unusual in the presented setting, and their cause is not understood.

References

We have no explanation for these successive saddle-node bifurcations.

— 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 4.2.6 (RPO29: saddle-node and global bifurcations)