Collective excitability in highly diluted random networks of oscillators

Year: 2022

Authors: Paolini G., Ciszak M., Marino F., Olmi S., Torcini A.

Autors Affiliation: Laboratoire de Physique Théorique et Modélisation, UMR 8089, CY Cergy Paris Université, CNRS, 95302 Cergy-Pontoise, France; CNR—Consiglio Nazionale delle Ricerche—Istituto Nazionale di Ottica, via Sansone 1, 50019 Sesto Fiorentino, Italy;
INFN, Sezione di Firenze, via Sansone 1, 50019 Sesto Fiorentino, Italy; CNR—Consiglio Nazionale delle Ricerche—Istituto dei Sistemi Complessi, via Madonna del Piano 10, 50019 Sesto Fiorentino, Italy

Abstract: We report on collective excitable events in a highly diluted random network of non-excitable nodes. Excitability arises thanks to a self-sustained local adaptation mechanism that drives the system on a slow timescale across a hysteretic phase transition involving states with different degrees of synchronization. These phenomena have been investigated for the Kuramoto model with bimodal distribution of the natural frequencies and for the Kuramoto model with inertia and a unimodal frequency distribution. We consider global and partial stimulation protocols and characterize the system response for different levels of dilution. We compare the results with those obtained in the fully coupled case showing that such collective phenomena are remarkably robust against network diluteness.

Journal/Review: CHAOS

Volume: 32 (10)      Pages from: 103108-1  to: 103108-12

More Information: A.T. received financial support from the Labex MME-DII (Grant No. ANR-11-LBX-0023-01) (together with MP) and from the ANR Project ERMUNDY (Grant No. ANR-18-CE37-0014), all part of the French program “Investissements d´Avenir.” Part of this work has been developed during the visit of SO during 2021 to the Maison internationale de La Recherche, Neuville-sur-Oise, France supported by CY Advanced Studies, CY Cergy Paris Universite, France.
KeyWords: Statistical analysis, Complex adaptive systems, Phase transitions,
Canard, Kuramoto models, Chaos synchronization

DOI: 10.1063/5.0102880