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arXiv · 1712.01616

Characterization of Fundamental Networks

Manuela A D Aguiar·Ana P S Dias·Pedro Soares
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Abstract

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 subspaces, each network admissible system restricted to that subspace is a dynamical systems consistent with a smaller network. The original network is then said to be a lift of the smaller network. We characterize networks such that: its fundamental network is a lift of the network; the network is a subnetwork of its fundamental network, and the network is a fundamental network. 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.

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BibTeXRIS

Manuela A D Aguiar, Ana P S Dias, Pedro Soares. 2017-12-05. Characterization of Fundamental Networks. https://arxiv.org/abs/1712.01616

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