Commutative Monoid Formalism for Weighted Coupled Cell Networks and Invariant Synchrony Patterns

Autor:	Pedro M. N. Sequeira, A.P. Aguiar, Joao P. Hespanha
Rok vydání:	2021
Předmět:	Set (abstract data type) Discrete mathematics 34A34 34C45 Computer science Formalism (philosophy) Modeling and Simulation Computer Science - Multiagent Systems Enhanced Data Rates for GSM Evolution Commutative monoid Mathematics - Dynamical Systems Invariant (mathematics) Analysis
Zdroj:	SIAM Journal on Applied Dynamical Systems. 20:1485-1513
ISSN:	1536-0040
DOI:	10.1137/20m1387109
Popis:	This paper presents a framework based on matrices of monoids for the study of coupled cell networks. We formally prove within the proposed framework, that the set of results about invariant synchrony patterns for unweighted networks also holds for the weighted case. Moreover, the approach described allows us to reason about any multiedge and multiedge-type network as if it was single edge and single-edge-type. Several examples illustrate the concepts described. Additionally, an improvement of the coarsest invariant refinement algorithm to find balanced partitions is presented that exhibits a worst-case complexity of $ \mathbf{O}(\vert\mathcal{C}\vert^3) $, where $\mathcal{C}$ denotes the set of cells. Comment: 29 pages, 7 figures
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::0934fdf4f593344b92145afc55d27eb4 https://doi.org/10.1137/20m1387109 Zobrazit plný text záznamu