On Discrete-Time Polynomial Dynamical Systems on Hypergraphs

被引：0

作者：

Cui, Shaoxuan ^{[1
]}

Zhang, Guofeng ^{[2
]}

Jardon-Kojakhmetov, Hildeberto ^{[1
]}

Cao, Ming ^{[3
]}

机构：

[1] Univ Groningen, Bernoulli Inst, NL-9747 AG Groningen, Netherlands

[2] Hong Kong Polytech Univ, Dept Appl Math, Hong Kong, Peoples R China

[3] Univ Groningen, ENTEG, NL-9747 AG Groningen, Netherlands

来源：

IEEE CONTROL SYSTEMS LETTERS | 2024年 / 8卷

关键词：

Tensors; Polynomials; Vectors; Tail; Stability criteria; Eigenvalues and eigenfunctions; Couplings; Hypergraphs; higher-order interactions; polynomial systems; Z-eigenvalues; Perron-Frobenius Theorem; stability; PERRON-FROBENIUS THEOREM; GLOBAL STABILITY;

D O I：

10.1109/LCSYS.2024.3406597

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This letter 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.

引用

页码：1078 / 1083

页数：6

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