Central Limit Behavior at the Edge of Chaos in the z-Logistic Map
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908493295910912 |
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| author | Saberi, Abbas Ali Tirnakli, Ugur Tsallis, Constantino |
| author_facet | Saberi, Abbas Ali Tirnakli, Ugur Tsallis, Constantino |
| contents | We focus on the FeigenbaumCoulletTresser point of the dissipative one-dimensional z logistic map. We show that sums of iterates converge to q Gaussian distributions, which optimize the nonadditive entropic functional Sq under simple constraints. We derive a closedform prediction for the entropic index, and validate it numerically via data collapse for typical z values. The formula captures how the limiting law depends on the nonlinearity order and implies finite variance for z larger than 2 and divergent variance for z in between 1 and 2. These results extend edge of chaos central limit behavior beyond the standard case and provide a simple predictive law for unimodal maps with varying maximum order. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_13170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Central Limit Behavior at the Edge of Chaos in the z-Logistic Map Saberi, Abbas Ali Tirnakli, Ugur Tsallis, Constantino Statistical Mechanics Chaotic Dynamics We focus on the FeigenbaumCoulletTresser point of the dissipative one-dimensional z logistic map. We show that sums of iterates converge to q Gaussian distributions, which optimize the nonadditive entropic functional Sq under simple constraints. We derive a closedform prediction for the entropic index, and validate it numerically via data collapse for typical z values. The formula captures how the limiting law depends on the nonlinearity order and implies finite variance for z larger than 2 and divergent variance for z in between 1 and 2. These results extend edge of chaos central limit behavior beyond the standard case and provide a simple predictive law for unimodal maps with varying maximum order. |
| title | Central Limit Behavior at the Edge of Chaos in the z-Logistic Map |
| topic | Statistical Mechanics Chaotic Dynamics |
| url | https://arxiv.org/abs/2508.13170 |