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

Otti D'Huys, Romain Veltz, Axel Dolcemascolo, Francesco Marino, Stephane Barland

Research output: Contribution to journalArticleAcademicpeer-review


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.

Original languageEnglish
Article number024010
Number of pages14
JournalJPhys Photonics
Issue number2
Publication statusPublished - Apr 2021

JEL classifications

  • c69 - "Mathematical Methods; Programming Models; Mathematical and Simulation Modeling: Other"


  • laser dynamics
  • slow-fast dynamical systems
  • stochastic differential equations
  • excitability
  • noise
  • semiconductor lasers
  • fully connected networks
  • slow-fast systems

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