Collective canard explosions of globally-coupled rotators with adaptive coupling
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866915658155950080 |
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| author | Ciszak, Marzena Olmi, Simona Innocenti, Giacomo Torcini, Alessandro Marino, Francesco |
| author_facet | Ciszak, Marzena Olmi, Simona Innocenti, Giacomo Torcini, Alessandro Marino, Francesco |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2110_10473 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Collective canard explosions of globally-coupled rotators with adaptive coupling Ciszak, Marzena Olmi, Simona Innocenti, Giacomo Torcini, Alessandro Marino, Francesco Adaptation and Self-Organizing Systems Disordered Systems and Neural Networks Dynamical Systems Chaotic Dynamics 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. |
| title | Collective canard explosions of globally-coupled rotators with adaptive coupling |
| topic | Adaptation and Self-Organizing Systems Disordered Systems and Neural Networks Dynamical Systems Chaotic Dynamics |
| url | https://arxiv.org/abs/2110.10473 |