Collective canard explosions of globally-coupled rotators with adaptive coupling

TL;DR

This paper demonstrates the emergence of collective canard explosions in a population of globally-coupled phase-rotators with adaptive coupling, revealing complex dynamics in mean-field models and large systems.

Contribution

It introduces the concept of collective canard explosions in adaptive coupled rotator systems and provides a geometric singular perturbation analysis of the mean-field model.

Findings

Collective canards occur in bimodal Kuramoto models with adaptive coupling.

The stability of the critical manifold explains the emergence of canards.

Large system sizes show gradual emergence of collective canards despite trivial individual dynamics.

Abstract

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.