Internal reliability and anti-reliability in dynamical networks
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917881991659520 |
|---|---|
| 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 |