Commutative monoid formalism for weighted coupled cell networks and invariant synchrony patterns

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Sequeira, PM (Author) Other; Aguiar, AP (Author) FEUP; Hespanha, J (Author) Other

Journal

Title: SIAM Journal on Applied Dynamical Systems

Vol. 20

Pages: 1485-1513

ISSN: 1536-0040

Publisher: Society for Industrial and Applied Mathematics

Indexing

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Other information

Authenticus ID: P-00V-EAG

DOI: 10.1137/20m1387109

Abstract (EN): 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 O lC|3), where C denotes the set of cells.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 29