Collective canard explosions of globally-coupled rotators with adaptive coupling

Year: 2021

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

Autors Affiliation: CNR, Ist Nazl Ott, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; CNR, Ist Sistemi Complessi, Via Madonna Piano 10, I-50019 Sesto Fiorentino, Italy; Ist Nazl Fis Nucl, Sez Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; Univ Florence, Dept Informat Engn, Via Santa Marta 3, I-50139 Florence, Italy; Univ Cergy Pontoise, CNRS, UMR 8089, Lab Phys Theor & Modelisat, F-95302 Cergy Pontoise, France.

Abstract: Canards, special trajectories that follow invariant repelling slow manifolds for long time intervals, have been frequently observed in slow-fast systems of either biological, chemical and physical nature. Here, collective canard explosions are demonstrated in a population of globally-coupled phase-rotators subject to adaptive coupling. In particular, we consider a bimodal Kuramoto model displaying coexistence of asynchronous and partially synchronized dynamics subject to a linear global feedback. A detailed geometric singular perturbation analysis of the associated mean-field model allows us to explain the emergence of collective canards in terms of the stability properties of the one-dimensional critical manifold, near which the slow macroscopic dynamics takes place. We finally show how collective canards and related manifolds gradually emerge in the globally-coupled system for increasing system sizes, in spite of the trivial dynamics of the uncoupled rotators.

Journal/Review: CHAOS SOLITONS & FRACTALS

Volume: 153 (1)      Pages from: 111592-1  to: 111592-8

KeyWords: emergent dynamics, network of phase-oscillators, canards, mean-field modelling, geometric singular perturbation, effective slow manifold
DOI: 10.1016/j.chaos.2021.111592

Citations: 6
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