On discrete-time polynomial dynamical systems on hypergraphs
arxiv(2024)
摘要
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. First of all, for a multilinear polynomial system on a uniform
hypergraph, we study the stability of the origin of the corresponding systems.
Afterward, 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. In
particular, given 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.
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