On Complexity of Stability Analysis in Higher-order Ecological Networks through Tensor Decompositions
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929301154168832 |
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| author | Dong, Anqi Chen, Can |
| author_facet | Dong, Anqi Chen, Can |
| contents | Complex ecological networks are often characterized by intricate interactions that extend beyond pairwise relationships. Understanding the stability of higher-order ecological networks is salient for species coexistence, biodiversity, and community persistence. In this article, we present complexity analyses for determining the linear stability of higher-order ecological networks through tensor decompositions. We are interested in the higher-order generalized Lotka-Volterra model, which captures high-order interactions using tensors of varying orders. To efficiently compute Jacobian matrices and thus determine stability in large ecological networks, we exploit various tensor decompositions, including higher-order singular value decomposition, Canonical Polyadic decomposition, and tensor train decomposition, accompanied by in-depth computational and memory complexity analyses. We demonstrate the effectiveness of our framework with numerical examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_02023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Complexity of Stability Analysis in Higher-order Ecological Networks through Tensor Decompositions Dong, Anqi Chen, Can Systems and Control Numerical Analysis Optimization and Control 93Dxx, 05C65, 92D40, 15A69 Complex ecological networks are often characterized by intricate interactions that extend beyond pairwise relationships. Understanding the stability of higher-order ecological networks is salient for species coexistence, biodiversity, and community persistence. In this article, we present complexity analyses for determining the linear stability of higher-order ecological networks through tensor decompositions. We are interested in the higher-order generalized Lotka-Volterra model, which captures high-order interactions using tensors of varying orders. To efficiently compute Jacobian matrices and thus determine stability in large ecological networks, we exploit various tensor decompositions, including higher-order singular value decomposition, Canonical Polyadic decomposition, and tensor train decomposition, accompanied by in-depth computational and memory complexity analyses. We demonstrate the effectiveness of our framework with numerical examples. |
| title | On Complexity of Stability Analysis in Higher-order Ecological Networks through Tensor Decompositions |
| topic | Systems and Control Numerical Analysis Optimization and Control 93Dxx, 05C65, 92D40, 15A69 |
| url | https://arxiv.org/abs/2401.02023 |