Mean-field and fluctuations for hub dynamics in heterogeneous random networks
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866918068519698432 |
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| author | Bian, Zheng Lamb, Jeroen S. W. Pereira, Tiago |
| author_facet | Bian, Zheng Lamb, Jeroen S. W. Pereira, Tiago |
| contents | In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically controlled fluctuations. In particular, we prove that the fluctuations are small over exponentially long time scales and obtain Berry-Esseen estimates for the fluctuation statistics at any fixed time. Our results provide a mathematical explanation for several numerical observations, including the scaling relation between system size and frequency of large fluctuations, as well as system size induced desynchronization. To our best knowledge, these are the first characterizations of mean-field fluctuations on networks with a degree distribution that follows a power-law, a common feature for many realistic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_11178 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean-field and fluctuations for hub dynamics in heterogeneous random networks Bian, Zheng Lamb, Jeroen S. W. Pereira, Tiago Dynamical Systems Mathematical Physics Probability 37A50, 37A60, 37B65, 37D20, 37E10, 37H12, 60F05, 60J05, 60J20, 60C05, 05C80, 82C99 G.3; I.6.3 In a class of heterogeneous random networks, where each node dynamics is a random dynamical system, interacting with neighbor nodes via a random coupling function, we characterize the hub behavior as the mean-field, subject to statistically controlled fluctuations. In particular, we prove that the fluctuations are small over exponentially long time scales and obtain Berry-Esseen estimates for the fluctuation statistics at any fixed time. Our results provide a mathematical explanation for several numerical observations, including the scaling relation between system size and frequency of large fluctuations, as well as system size induced desynchronization. To our best knowledge, these are the first characterizations of mean-field fluctuations on networks with a degree distribution that follows a power-law, a common feature for many realistic systems. |
| title | Mean-field and fluctuations for hub dynamics in heterogeneous random networks |
| topic | Dynamical Systems Mathematical Physics Probability 37A50, 37A60, 37B65, 37D20, 37E10, 37H12, 60F05, 60J05, 60J20, 60C05, 05C80, 82C99 G.3; I.6.3 |
| url | https://arxiv.org/abs/2408.11178 |