Canard cascading in networks with adaptive mean-field coupling
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arXiv
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| Auteurs principaux: | , , , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917737443360768 |
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| author | Balzer, Juan Berner, Rico Lüdge, Kathy Wieczorek, Sebastian Kurths, Jürgen Yanchuk, Serhiy |
| author_facet | Balzer, Juan Berner, Rico Lüdge, Kathy Wieczorek, Sebastian Kurths, Jürgen Yanchuk, Serhiy |
| contents | Canard cascading (CC) is observed in dynamical networks with global adaptive coupling. It is a fast-slow phenomenon characterized by a recurrent sequence of fast transitions between distinct and slowly evolving quasi-stationary states. In this letter, we uncover the dynamical mechanisms behind CC, using an illustrative example of globally and adaptively coupled semiconductor lasers, where CC represents sequential switching on and off the lasers. Firstly, we show that CC is a robust and truly adaptive network effect that is scalable with network size and does not occur without adaptation. Secondly, we uncover multiple saddle slow manifolds (unstable quasi-stationary states) linked by heteroclinic orbits (fast transitions) in the phase space of the system. This allows us to identify CC with a novel heteroclinic canard orbit that organises different unstable quasi-stationary states into an intricate fast-slow limit cycle. Although individual quasi-stationary states are unstable (saddles), the CC cycle as a whole is attractive and robust to parameter changes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_20758 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Canard cascading in networks with adaptive mean-field coupling Balzer, Juan Berner, Rico Lüdge, Kathy Wieczorek, Sebastian Kurths, Jürgen Yanchuk, Serhiy Adaptation and Self-Organizing Systems Pattern Formation and Solitons Canard cascading (CC) is observed in dynamical networks with global adaptive coupling. It is a fast-slow phenomenon characterized by a recurrent sequence of fast transitions between distinct and slowly evolving quasi-stationary states. In this letter, we uncover the dynamical mechanisms behind CC, using an illustrative example of globally and adaptively coupled semiconductor lasers, where CC represents sequential switching on and off the lasers. Firstly, we show that CC is a robust and truly adaptive network effect that is scalable with network size and does not occur without adaptation. Secondly, we uncover multiple saddle slow manifolds (unstable quasi-stationary states) linked by heteroclinic orbits (fast transitions) in the phase space of the system. This allows us to identify CC with a novel heteroclinic canard orbit that organises different unstable quasi-stationary states into an intricate fast-slow limit cycle. Although individual quasi-stationary states are unstable (saddles), the CC cycle as a whole is attractive and robust to parameter changes. |
| title | Canard cascading in networks with adaptive mean-field coupling |
| topic | Adaptation and Self-Organizing Systems Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2407.20758 |