Basins of Attraction

High-dimensional basins

How do basins look like in high-dimensional systems?

• Y. Zhang and S. H. Strogatz, Basins with tentacles, Phys. Rev. Lett. 127, 194101 (2021)

Do higher-order interactions expand or shrink basins?

• Y. Zhang, P. S. Skardal, F. Battiston, G. Petri, and M. Lucas, Deeper but smaller: Higher-order interactions increase linear stability but shrink basins, Sci. Adv. 10, ado8049 (2024)

How do basin sizes scale?

• P. Groisman, C. De Vita, J. F. Bonder, and Y. Zhang†, The size of the sync basin resolved, arXiv:2506.034199

Fractal basins

Can we learn complicated basins from data using machine learning?

• Y. Zhang and S. P. Cornelius, Catch-22s of reservoir computing, Phys. Rev. Research 5, 033213 (2023)
• D. A. Norton, Y. Zhang, and M. Girvan, Learning Beyond Experience: Generalizing to Unseen State Space with Reservoir Computing, arXiv:2506.05292

Can intermingled basins give rise to non-exponetial transition statistics?

• Y. Zhang, Z. G. Nicolaou, J. D. Hart, R. Roy, and A. E. Motter, Critical switching in globally attractive chimeras, Phys. Rev. X 10, 011044 (2020)