Emergent excitability in populations of nonexcitable units

Year: 2020

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

Autors Affiliation: CNR Consiglio Nazl Ric, Ist Nazl Ott, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; Ist Nazl Fis Nucl, Sez Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; Univ Cergy Pontoise, Lab Phys Theor & Modelisat, CNRS, UMR 8089, F-95302 Cergy Pontoise, France; CNR Consiglio Nazl Ric, Ist Sistemi Complessi, Via Madonna Piano 10, I-50019 Sesto Fiorentino, Italy; INRIA, Sophia Antipolis Mediterranee Res Ctr, 2004 Route 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.

Journal/Review: PHYSICAL REVIEW E

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 dŽAvenir.
KeyWords: Bifurcations, Chaos, Collective dynamics, Coupled oscillators, Synchronization transition, Excitability
DOI: 10.1103/PhysRevE.102.050201

Citations: 9
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