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Canard Cascading in Networks with Adaptive Mean-Field Coupling.

J Balzer1, R Berner2, K Lüdge3

  • 1Institut für Theoretische Physik, <a href="https://ror.org/03v4gjf40">Technische Universität Berlin</a>, Hardenbergstraße 36, 10623 Berlin, Germany.

Physical Review Letters
|December 23, 2024
PubMed
Summary
This summary is machine-generated.

Canard cascading (CC) in adaptive networks involves slow-fast dynamics. Researchers identified novel mechanisms, revealing CC as a robust, scalable network effect driven by heteroclinic canard orbits.

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Area of Science:

  • Dynamical systems
  • Network science
  • Nonlinear dynamics

Background:

  • Canard cascading (CC) is a slow-fast phenomenon in adaptive dynamical networks.
  • It involves recurrent fast transitions between slowly evolving quasistationary states.
  • CC has been observed in systems like coupled semiconductor lasers.

Purpose of the Study:

  • To uncover the dynamical mechanisms underlying Canard Cascading (CC).
  • To investigate CC in globally and adaptively coupled semiconductor lasers.
  • To demonstrate CC as a robust and scalable network effect.

Main Methods:

  • Analysis of slow-fast dynamical systems.
  • Phase space exploration to identify manifolds and orbits.
  • Utilizing semiconductor laser networks as a model system.

Main Results:

  • CC is a robust, scalable network effect unique to adaptive coupling.
  • Multiple saddle slow manifolds linked by heteroclinic orbits were identified.
  • CC was characterized as a novel heteroclinic canard orbit organizing unstable states into an attractive limit cycle.

Conclusions:

  • The study elucidates the mechanisms driving Canard Cascading.
  • CC is a robust phenomenon arising from the interplay of adaptation and network structure.
  • The findings offer insights into complex behaviors in adaptive dynamical networks.