Resonant Solitary States in Complex Networks
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arXiv
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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910707590627328 |
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| author | Niehues, Jakob Yanchuk, Serhiy Berner, Rico Kurths, Jürgen Hellmann, Frank Anvari, Mehrnaz |
| author_facet | Niehues, Jakob Yanchuk, Serhiy Berner, Rico Kurths, Jürgen Hellmann, Frank Anvari, Mehrnaz |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_06483 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Resonant Solitary States in Complex Networks Niehues, Jakob Yanchuk, Serhiy Berner, Rico Kurths, Jürgen Hellmann, Frank Anvari, Mehrnaz Adaptation and Self-Organizing Systems Applied Physics 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. |
| title | Resonant Solitary States in Complex Networks |
| topic | Adaptation and Self-Organizing Systems Applied Physics |
| url | https://arxiv.org/abs/2401.06483 |