Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Collective canard explosions of globally-coupled rotators with adaptive
  coupling   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.

32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
35
The categories of this paper are: mtrl-th
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs