Emergent excitability in populations of nonexcitable units

Year: 2020

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

Autors Affiliation: CNR – Consiglio Nazionale delle Ricerche – Istituto Nazionale di Ottica, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy; INFN, Sezione di Firenze, Via Sansone 1, I-50019 Sesto Fiorentino (FI), Italy; Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, CNRS, UMR 8089,F-95302 Cergy-Pontoise Cedex, France; CNR – Consiglio Nazionale delle Ricerche – Istituto dei Sistemi Complessi, via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy5Inria Sophia Antipolis Méditerranée Research Centre, 2004 Route des Lucioles, F-06902 Valbonne, France

Abstract: Population bursts in a large ensemble of coupled elements result from the interplay between the local excitable properties of the nodes and the global network topology. Here, collective excitability and self-sustained bursting oscillations are shown to spontaneously emerge in globally coupled populations of nonexcitable units subject to adaptive coupling. The ingredients to observe collective excitability are the coexistence of states with different degrees of synchronization joined to a global feedback acting, on a slow timescale, against the synchronization (desynchronization) of the oscillators. These regimes are illustrated for two paradigmatic classes of coupled rotators, namely, the Kuramoto model with and without inertia. For the bimodal Kuramoto model we analytically show that the macroscopic evolution originates from the existence of a critical manifold organizing the fast collective dynamics on a slow timescale. Our results provide evidence that adaptation can induce excitability by maintaining a network permanently out of equilibrium.


Volume: 102      Pages from: 050201-1  to: 050201-6

More Information: We acknowledge Veronica and Milena Marino for lively and animated discussions. A.T. received financial support by the Excellence Initiative I-Site Paris Seine (Grant No. ANR-16-IDEX-008), by the Labex MME-DII (Grant No. ANR-11-LBX-0023-01), and by the ANR Project ERMUNDY (Grant No. ANR-18-CE37-0014), all part of the French program Investissements d´Avenir.
KeyWords: Bifurcations, Chaos, Collective dynamics, Coupled oscillators, Synchronization transition, Excitability
DOI: 10.1103/PhysRevE.102.050201

Citations: 9
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