  Canards, special trajectories that follow invariant repelling slow manifolds
for long time intervals, have been frequently observed in slow-fast systems of
either biological, chemical and physical nature. Here, collective canard
explosions are demonstrated in a population of globally-coupled phase-rotators
subject to adaptive coupling. In particular, we consider a bimodal Kuramoto
model displaying coexistence of asynchronous and partially synchronized
dynamics subject to a linear global feedback. A detailed geometric singular
perturbation analysis of the associated mean-field model allows us to explain
the emergence of collective canards in terms of the stability properties of the
one-dimensional critical manifold, near which the slow macroscopic dynamics
takes place. We finally show how collective canards and related manifolds
gradually emerge in the globally-coupled system for increasing system sizes, in
spite of the trivial dynamics of the uncoupled rotators.
