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Characterization of fundamental networks

Title
Characterization of fundamental networks
Type
Article in International Scientific Journal
Year
2020-02-01
Authors
Manuela Aguiar
(Author)
FEP
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dias, aps
(Author)
FCUP
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Soares, P
(Author)
Other
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Journal
Vol. 150 No. 1
Pages: 453-474
ISSN: 0308-2105
Other information
Authenticus ID: P-00Q-5QY
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
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