Internal reliability and anti-reliability in dynamical networks
Abstract
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.
Cite
@article{arxiv.2501.00079,
title = {Internal reliability and anti-reliability in dynamical networks},
author = {Tommaso Matteuzzi and Franco Bagnoli and Michele Baia and Stefano Iubini and Arkady Pikovsky},
journal= {arXiv preprint arXiv:2501.00079},
year = {2025}
}