Canard Cascading in Networks with Adaptive Mean-Field Coupling

Canard cascading (CC) is observed in dynamical networks with global adaptive coupling. It is a slow-fast phenomenon characterized by a recurrent sequence of fast transitions between distinct and slowly evolving quasistationary states. In this Letter, we uncover the dynamical mechanisms behind CC, using an illustrative example of globally and adaptively coupled semiconductor lasers, where CC represents sequential switching on and off the lasers. First, we show that CC is a robust and truly adaptive network effect that is scalable with network size and does not occur without adaptation. Second, we uncover multiple saddle slow manifolds (unstable quasistationary states) linked by heteroclinic orbits (fast transitions) in the phase space of the system. This allows us to identify CC with a novel heteroclinic canard orbit that organizes different unstable quasistationary states into an intricate slow-fast limit cycle. Although individual quasistationary states are unstable (saddles), the CC cycle as a whole is attractive and robust to parameter changes.