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Resonant Solitary States in Complex Networks

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Jakob Niehues, Serhiy Yanchuk, Rico Berner, Jürgen Kurths, Frank Hellmann, Mehrnaz Anvari

Adaptation and Self-Organizing Systems · Submitted 12 Jan 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our framework unifies the description of solitary states near and far from resonance, allowing to predict the behavior of complex networks.

how it is stated · asserted 1.00 read the record →

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arXiv ID2401.06483 (version 3)
Pith ID7I6FQS6F, Pith's permanent record of this paper and its review
CitationFrank Hellmann, Jakob Niehues, J\"urgen Kurths, Mehrnaz Anvari, Rico Berner, Serhiy Yanchuk. "Resonant Solitary States in Complex Networks." arXiv:2401.06483 (2024). https://pith.science/paper/7I6FQS6F
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,424 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.22 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

Partially synchronized solitary states occur frequently when a synchronized system of networked oscillators is perturbed locally. Several asymptotic states of different frequencies can coexist at the same node. Here, we reveal the mechanism behind this multistability: additional solitary frequencies arise from the coupling between network modes and the solitary oscillator's frequency, leading to significant energy transfer. This can cause the solitary node's frequency to resonate with a Laplacian eigenvalue. We analyze which network structures enable this resonance and explain longstanding numerical observations. Another solitary state is characterized by the effective decoupling of the synchronized network and the solitary node at the natural frequency. Our framework unifies the description of solitary states near and far from resonance, allowing to predict the behavior of complex networks.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 Partially synchronized solitary states occur frequently when a synchronized system of networked oscillators is perturbed locally. background 0.99 0.16 0.05 asserted 0.99
s1 Several asymptotic states of different frequencies can coexist at the same node. background 0.73 0.26 0.05 asserted 0.98
s2 Here, we reveal the mechanism behind this multistability: additional solitary frequencies arise from the coupling between network modes and the solitary oscillator's frequency, leading to significant energy transfer. contribution 0.50 0.90 0.70 asserted 1.00
s3 This can cause the solitary node's frequency to resonate with a Laplacian eigenvalue. interpretation 0.64 0.54 0.13 hedged possibility 0.79
s4 We analyze which network structures enable this resonance and explain longstanding numerical observations. contribution 0.97 0.91 0.10 asserted 0.98
s5 Another solitary state is characterized by the effective decoupling of the synchronized network and the solitary node at the natural frequency. result 0.97 0.58 0.08 asserted 1.00
s6 Our framework unifies the description of solitary states near and far from resonance, allowing to predict the behavior of complex networks. contribution 0.77 0.89 0.58 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.82.

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  • full text
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  • references and citing sentences
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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

Partially synchronized solitary states occur frequently when a synchronized system of networked oscillators is perturbed locally. Several asymptotic states of different frequencies can coexist at the same node. Here, we reveal the mechanism behind this multistability: additional solitary frequencies arise from the coupling between network modes and the solitary oscillator's frequency, leading to significant energy transfer. This can cause the solitary node's frequency to resonate with a Laplacian eigenvalue. We analyze which network structures enable this resonance and explain longstanding numerical observations. Another solitary state is characterized by the effective decoupling of the synchronized network and the solitary node at the natural frequency. Our framework unifies the description of solitary states near and far from resonance, allowing to predict the behavior of complex networks.

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