Characterization of fundamental networks

• Type: Article in International Scientific Journal
• Date: 2020-02-01

Authors

Manuela Aguiar (Author) FEP; dias, aps (Author) FCUP; Soares, P (Author) Other

Journal

Title: Proceedings of the Royal Society of Edinburgh Section A: Mathematics

Vol. 150 No. 1

Pages: 453-474

ISSN: 0308-2105

Publisher: Cambridge University Press

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00Q-5QY

DOI: 10.1017/prm.2018.71

Abstract (EN): In the framework of coupled cell systems, a coupled cell network describes graphically the dynamical dependencies between individual dynamical systems, the cells. The fundamental network of a network reveals the hidden symmetries of that network. Subspaces defined by equalities of coordinates which are flow-invariant for any coupled cell system consistent with a network structure are called the network synchrony subspaces. Moreover, for every synchrony subspace, each network admissible system restricted to that subspace is a dynamical system consistent with a smaller network called a quotient network. We characterize networks such that: the network is a subnetwork of its fundamental network, and the network is a fundamental network. Moreover, we prove that the fundamental network construction preserves the quotient relation and it transforms the subnetwork relation into the quotient relation. The size of cycles in a network and the distance of a cell to a cycle are two important properties concerning the description of the network architecture. In this paper, we relate these two architectural properties in a network and its fundamental network. © 2019 Royal Society of Edinburgh.

Language: English

Type (Professor's evaluation): Scientific