Internal reliability and anti-reliability in dynamical networks

Fuente: arXiv
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Main Authors: Matteuzzi, Tommaso, Bagnoli, Franco, Baia, Michele, Iubini, Stefano, Pikovsky, Arkady
Format: Preprint
Published: 2024
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author Matteuzzi, Tommaso
Bagnoli, Franco
Baia, Michele
Iubini, Stefano
Pikovsky, Arkady
author_facet Matteuzzi, Tommaso
Bagnoli, Franco
Baia, Michele
Iubini, Stefano
Pikovsky, Arkady
contents We consider finite dynamical networks and define internal reliability according to the synchronization properties of a replicated unit or a set of units. If the states of the replicated units coincide with their prototypes, they are reliable; otherwise, if their states differ, they are anti-reliable. Quantification of reliability with the transversal Lyapunov exponent allows for a straightforward analysis of different models. For a Kuramoto model of globally coupled phase oscillators with a distribution of natural frequencies, we show that prior to the onset of synchronization, peripheral in frequency units are anti-reliable, while central are reliable. For this model, reliability can be expressed via phase correlations in a sort of a fluctuation-dissipation relation. Sufficiently large sub-networks in the Kuramoto model are always anti-reliable; the same holds for a recurrent neural network, where individual units are always reliable.
format Preprint
id arxiv_https___arxiv_org_abs_2501_00079
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Internal reliability and anti-reliability in dynamical networks
Matteuzzi, Tommaso
Bagnoli, Franco
Baia, Michele
Iubini, Stefano
Pikovsky, Arkady
Adaptation and Self-Organizing Systems
We consider finite dynamical networks and define internal reliability according to the synchronization properties of a replicated unit or a set of units. If the states of the replicated units coincide with their prototypes, they are reliable; otherwise, if their states differ, they are anti-reliable. Quantification of reliability with the transversal Lyapunov exponent allows for a straightforward analysis of different models. For a Kuramoto model of globally coupled phase oscillators with a distribution of natural frequencies, we show that prior to the onset of synchronization, peripheral in frequency units are anti-reliable, while central are reliable. For this model, reliability can be expressed via phase correlations in a sort of a fluctuation-dissipation relation. Sufficiently large sub-networks in the Kuramoto model are always anti-reliable; the same holds for a recurrent neural network, where individual units are always reliable.
title Internal reliability and anti-reliability in dynamical networks
topic Adaptation and Self-Organizing Systems
url https://arxiv.org/abs/2501.00079