On discrete-time polynomial dynamical systems on hypergraphs
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914824385986560 |
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| author | Cui, Shaoxuan Zhang, Guofeng Jardón-Kojakhmetov, Hildeberto Cao, Ming |
| author_facet | Cui, Shaoxuan Zhang, Guofeng Jardón-Kojakhmetov, Hildeberto Cao, Ming |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03416 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On discrete-time polynomial dynamical systems on hypergraphs Cui, Shaoxuan Zhang, Guofeng Jardón-Kojakhmetov, Hildeberto Cao, Ming Systems and Control 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. |
| title | On discrete-time polynomial dynamical systems on hypergraphs |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2403.03416 |