# On discrete-time polynomial dynamical systems on hypergraphs

arXiv: https://arxiv.org/abs/2403.03416 · HTML: https://mlsanity.com/paper/2403.03416/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Structural Controllability of Large-Scale Hypergraphs](https://mlsanity.com/paper/2603.19955/) (2026)

## Abstract (arXiv)

This paper studies the stability of discrete-time polynomial dynamical systems on hypergraphs by utilizing the Perron-Frobenius theorem for nonnegative tensors with respect to the tensors Z-eigenvalues and Z-eigenvectors. Firstly, for a multilinear polynomial system on a uniform hypergraph, we study the stability of the origin of the corresponding systems. Next, we extend our results to non-homogeneous polynomial systems on non-uniform hypergraphs. We confirm that the local stability of any discrete-time polynomial system is in general dominated by pairwise terms. Assuming that the origin is locally stable, we construct a conservative (but explicit) region of attraction from the system parameters. Finally, we validate our results via some numerical examples.