Decomposition of Admissible Functions in Weighted Coupled Cell Networks

• Type: Article in International Scientific Journal
• Date: 2023

Authors

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

Journal

Title: SIAM Journal on Applied Dynamical Systems

Vol. 22

Pages: 1114-1152

ISSN: 1536-0040

Publisher: Society for Industrial and Applied Mathematics

Indexing

ISI Web of Knowledge - 0 Citations

Scopus - 0 Citations

Other information

Authenticus ID: P-00Y-HM2

DOI: 10.1137/22m1471328

Abstract (EN): This work makes explicit the degrees of freedom involved in modeling the dynamics of a network, or some other first-order property of a network, such as a measurement function. In previous work, an admissible function in a network was constructed through the evaluation of what we called oracle components. These oracle components are defined through some minimal properties that they are expected to obey. This is a high-level description in the sense that it is not clear how one could design such an object. The goal is to obtain a low-level representation of these objects by unwrapping them into their degrees of freedom. To achieve this, we introduce two decompositions. The first one is the more intuitive one and allows us to define the important concept of coupling order. The second decomposition is built on top of the first one and is valid for the class of coupling components that have finite coupling order. Despite this requirement, we show that this is still a very useful tool for designing coupling components with infinite coupling orders, through a limit approach.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 39