Dr. Yuanzhao Zhang, Santa Fe Institute

"Twists, triangles, and tentacles: A guided tour of highdimensional basins in networked dynamical systems"

Abstract: In this talk, I will explore the interesting geometries that emerge in high-dimensional attraction basins, which arise naturally in networked dynamical systems. Specifically, I will consider simple networks of coupled Kuramoto oscillators and show that the basins for the so-called twisted states cannot be approximated by simple convex shapes. Instead, they have tentacle-like structures where most of the basin volume is concentrated. Next, I will show that introducing non-pairwise couplings can make basins deeper but smaller—the states become linearly more stable but much harder to find due to basins shrinking dramatically. Time allowing, I will also comment on some challenges faced by popular machine learning techniques (e.g., reservoir computing) in learning the basins (and dynamics) of multistable dynamical systems.