Correlation time in extremal self-organized critical models

Rahul Chhimpa (), Abha Singh () and Avinash Chand Yadav ()
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Rahul Chhimpa: Banaras Hindu University
Abha Singh: Banaras Hindu University
Avinash Chand Yadav: Banaras Hindu University

The European Physical Journal B: Condensed Matter and Complex Systems, 2025, vol. 98, issue 6, 1-8

Abstract: Abstract We investigate correlation time numerically in extremal self-organized critical models, namely the Bak–Sneppen evolution and the Robin Hood dynamics. The (fitness) correlation time is the duration required for the extinction or mutation of species over the entire spatial region in the critical state. We apply the methods of finite-size scaling and extreme value theory to understand the statistics of the correlation time. We find power-law system size scaling behaviors for the mean, the variance, the mode, and the peak probability of the correlation time. We obtain data collapse for the correlation time cumulative probability distribution, and the scaling function follows the generalized extreme value density close to the Gumbel function. Graphic abstract

Date: 2025
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DOI: 10.1140/epjb/s10051-025-00988-1

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