Canard resonance: on noise-induced ordering of trajectories in heterogeneous networks of slow-fast systems

Year: 2021

Authors: D’Huys O., Veltz R., Dolcemascolo A., Marino F., Barland S.

Autors Affiliation: Aston Univ, Dept Math, Birmingham B4 7ET, W Midlands, England; Inria Sophia Antipolis, MathNeuro Team, 2004 Route Lucioles,BP93, F-06902 Sophia Antipolis, France; Univ Cote Azur, CNRS, INPHYNI, 1361 Route Lucioles, F-06560 Valbonne, France; CNR, Ist Nazl Ott, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; INFN, Sez Firenze, Via Sansone 1, I-50019 Sesto Fiorentino, FI, Italy; Maastricht Univ, Dept Data Sci Knowledge Engn, Maastricht, Netherlands.

Abstract: We analyse the dynamics of a network of semiconductor lasers coupled via their mean intensity through a non-linear optoelectronic feedback loop. We establish experimentally the excitable character of a single node, which stems from the slow-fast nature of the system, adequately described by a set of rate equations with three well separated time scales. Beyond the excitable regime, the system undergoes relaxation oscillations where the nodes display canard dynamics. We show numerically that, without noise, the coupled system follows an intricate canard trajectory, with the nodes switching on one by one. While incorporating noise leads to a better correspondence between numerical simulations and experimental data, it also has an unexpected ordering effect on the canard orbit, causing the nodes to switch on closer together in time. We find that the dispersion of the trajectories of the network nodes in phase space is minimized for a non-zero noise strength, and call this phenomenon canard resonance.

Journal/Review: JOURNAL OF PHYSICS-PHOTONICS

Volume: 3 (2)      Pages from: 24010-1  to: 24010-14

More Information: O D has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie Grant Agreement No. 713694.
KeyWords: slow-fast systems; semiconductor lasers; noise; excitability; fully connected networks
DOI: 10.1088/2515-7647/abcbe3

Citations: 4
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