Fitness noise in the Bak-Sneppen evolution model in high dimensions
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| Format: | Preprint |
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2024
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| _version_ | 1866929357422854144 |
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| author | Chhimpa, Rahul Singh, Abha Yadav, Avinash Chand |
| author_facet | Chhimpa, Rahul Singh, Abha Yadav, Avinash Chand |
| contents | We study the Bak-Sneppen evolution model on a regular hypercubic lattice in high dimensions. Recent work [Phys. Rev. E 108, 044109 (2023)] has shown the emergence of the $1/f^α$ noise for the ``fitness'' observable with $α\approx 1.2$ in one-dimension (1D) and $α\approx 2$ for the random neighbor (mean-field) version of the model. We examine the temporal correlation of fitness in 2, 3, and 4 dimensions. As obtained by finite-size scaling, the spectral exponent tends to take the mean-field value at the upper critical dimension ${\rm D}_u = 4$, which is consistent with previous studies. Our approach provides an alternative way to understand the upper critical dimension of the model. We also show the local activity power spectra, which offer insight into return time statistics and the avalanche dimension. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15255 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fitness noise in the Bak-Sneppen evolution model in high dimensions Chhimpa, Rahul Singh, Abha Yadav, Avinash Chand Statistical Mechanics We study the Bak-Sneppen evolution model on a regular hypercubic lattice in high dimensions. Recent work [Phys. Rev. E 108, 044109 (2023)] has shown the emergence of the $1/f^α$ noise for the ``fitness'' observable with $α\approx 1.2$ in one-dimension (1D) and $α\approx 2$ for the random neighbor (mean-field) version of the model. We examine the temporal correlation of fitness in 2, 3, and 4 dimensions. As obtained by finite-size scaling, the spectral exponent tends to take the mean-field value at the upper critical dimension ${\rm D}_u = 4$, which is consistent with previous studies. Our approach provides an alternative way to understand the upper critical dimension of the model. We also show the local activity power spectra, which offer insight into return time statistics and the avalanche dimension. |
| title | Fitness noise in the Bak-Sneppen evolution model in high dimensions |
| topic | Statistical Mechanics |
| url | https://arxiv.org/abs/2405.15255 |