Full orbit diagram and route-to-chaos characterization for Multilayer Triadic Percolation

Characterize the full orbit diagram and derive the route-to-chaos scenario for the Multilayer Triadic Percolation model across the control parameter p, extending beyond fixed-point bifurcation analysis to fully describe the dynamical regimes and transitions.

Background

Throughout the paper, the analysis focuses on fixed-point bifurcations (discontinuous, period-doubling, and Neimark–Sacker) in MTP. The authors explicitly state that a comprehensive characterization of the orbit diagram and the full route-to-chaos dynamics is not provided here and will be pursued in future work.

This open problem aims to complete the dynamical picture by mapping out the entire orbit structure and determining the global route-to-chaos behavior of MTP.

References

The analyses are restricted to the bifurcation of fixed points in parameter space. The characterisation of the full orbit diagram and the route to chaos will be left for future work.

— Triadic percolation on multilayer networks (2510.09341 - Sun et al., 10 Oct 2025) in Section “Conclusion”