On discrete-time polynomial dynamical systems on hypergraphs
<|reference_start|>On discrete-time polynomial dynamical systems on hypergraphs: 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.<|reference_end|>
@article{cui2024on,
    title={On discrete-time polynomial dynamical systems on hypergraphs},
    author={Shaoxuan Cui, Guofeng Zhang, Hildeberto Jard'on-Kojakhmetov, Ming Cao},
    journal={arXiv preprint arXiv:2403.03416},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.03416},
    primaryClass={eess.SY cs.SY}
}