On Complexity of Stability Analysis in Higher-order Ecological Networks through Tensor Decompositions

Autor:	Dong, Anqi, Chen, Can
Rok vydání:	2024
Předmět:	Electrical Engineering and Systems Science - Systems and Control Mathematics - Numerical Analysis Mathematics - Optimization and Control 93Dxx 05C65 92D40 15A69
Druh dokumentu:	Working Paper
Popis:	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. Comment: 6 pages, 3 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2401.02023 Zobrazit plný text záznamu View this record from Arxiv