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.

Collective canard explosions of globally-coupled rotators with adaptive coupling / Ciszak M.; Olmi S.; Innocenti G.; Torcini A.; Marino F.. - In: CHAOS, SOLITONS AND FRACTALS. - ISSN 0960-0779. - ELETTRONICO. - 153:(2021), pp. 111592.1-111592.8. [10.1016/j.chaos.2021.111592]

Collective canard explosions of globally-coupled rotators with adaptive coupling

Innocenti G.
;
2021

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.
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Ciszak M.; Olmi S.; Innocenti G.; Torcini A.; Marino F.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1289740
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