Scientific Results

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 – Consiglio Nazionale delle Ricerche – Istituto Nazionale di Ottica, Via Sansone 1, Sesto Fiorentino (FI) I-50019, Italy; CNR – Consiglio Nazionale delle Ricerche – Istituto dei Sistemi Complessi, via Madonna del Piano 10, Sesto Fiorentino I-50019, Italy; INFN, Sezione di Firenze, Via Sansone 1, Sesto Fiorentino (FI) I-50019, Italy; Department of Industrial Engineering, University of Florence, via di Santa Marta 3, Florence 50139, Italy; Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise,CNRS, UMR 8089, Cergy-Pontoise cedex 95302, 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 AND 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

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