##### Department of Mathematics,

University of California San Diego

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### Mathematics Colloquium

## Dr. Yuanzhao Zhang

#### Santa Fe Institute

## Twists, triangles, and tentacles: A guided tour of high-dimensional basins in networked dynamical systems

##### Abstract:

In this talk, I will explore the interesting geometries that emerge in high-dimensional attraction basins, which are important in applications such as protein folding, cell differentiation, and neural networks. As a paradigmatic model, I will consider networks of coupled Kuramoto oscillators and show that high-dimensional basins generally 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 among Kuramoto oscillators can make basins deeper but smallerâ€”the attractors become linearly more stable but much harder to find due to basins shrinking dramatically. Time allowing, I will also briefly mention a few related projects, including learning basins with reservoir computing and modeling circadian clocks with Kuramoto oscillators.

Host: Natalia Komarova

### December 4, 2023

### 4:00 PM

APM 6402

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