Phase and gain stability for adaptive dynamical networks.
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PubMed
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| Autori principali: | , , , , |
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| Natura: | Artículo científico |
| Lingua: | en |
| Pubblicazione: |
Chaos (Woodbury, N.Y.)
2025
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| Accesso online: | |
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| _version_ | 1868266204019294209 |
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| author | Kastendiek, Nina Niehues, Jakob Delabays, Robin Gross, Thilo Hellmann, Frank |
| author_facet | Kastendiek, Nina Niehues, Jakob Delabays, Robin Gross, Thilo Hellmann, Frank Kastendiek, Nina Niehues, Jakob Delabays, Robin Gross, Thilo Hellmann, Frank |
| collection | PubMed - marine biology |
| contents | Phase and gain stability for adaptive dynamical networks. Kastendiek, Nina Niehues, Jakob Delabays, Robin Gross, Thilo Hellmann, Frank In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of feedback systems from control theory, we derive local, sufficient conditions for steady states of such systems to be linearly stable. These conditions are local in the sense that they are written entirely in terms of the (linearized) behavior of the edges and nodes. We apply these conditions to the Kuramoto model with inertia written in an adaptive form and the adaptive Kuramoto model. For the former, we recover a classic result, and for the latter, we show that our sufficient conditions match necessary conditions where the latter are available, thus completely settling the question of linear stability in this setting. The method we introduce can be readily applied to a vast class of systems. It enables straightforward evaluation of stability in highly heterogeneous systems. |
| format | Artículo científico |
| id | pubmed_40358384 |
| institution | PubMed |
| language | en |
| publishDate | 2025 |
| publisher | Chaos (Woodbury, N.Y.) |
| record_format | pubmed |
| spellingShingle | Phase and gain stability for adaptive dynamical networks. Kastendiek, Nina Niehues, Jakob Delabays, Robin Gross, Thilo Hellmann, Frank Phase and gain stability for adaptive dynamical networks. Kastendiek, Nina Niehues, Jakob Delabays, Robin Gross, Thilo Hellmann, Frank In adaptive dynamical networks, the dynamics of the nodes and the edges influence each other. We show that we can treat such systems as a closed feedback loop between edge and node dynamics. Using recent advances on the stability of feedback systems from control theory, we derive local, sufficient conditions for steady states of such systems to be linearly stable. These conditions are local in the sense that they are written entirely in terms of the (linearized) behavior of the edges and nodes. We apply these conditions to the Kuramoto model with inertia written in an adaptive form and the adaptive Kuramoto model. For the former, we recover a classic result, and for the latter, we show that our sufficient conditions match necessary conditions where the latter are available, thus completely settling the question of linear stability in this setting. The method we introduce can be readily applied to a vast class of systems. It enables straightforward evaluation of stability in highly heterogeneous systems. |
| title | Phase and gain stability for adaptive dynamical networks. |
| url | https://pubmed.ncbi.nlm.nih.gov/40358384/ |