Canard Cascading in Networks with Adaptive Mean-Field Coupling

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.