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Multifractal fluctuations in zebrafish (Danio rerio) polarization time series

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Abstract

In this work, we study the polarization time series obtained from experimental observation of a group of zebrafish (Danio rerio) confined in a circular tank. The complex dynamics of the individual trajectory evolution lead to the appearance of multiple characteristic scales. Employing the Multifractal Detrended Fluctuation Analysis (MF-DFA), we found distinct behaviors according to the parameters used. The polarization time series are multifractal at low fish densities and their average scales with \(\rho ^{-1/4}\). On the other hand, they tend to be monofractal, and their average scales with \(\rho ^{-1/2}\) for high fish densities. These two regimes overlap at critical density \(\rho _c\), suggesting the existence of a phase transition separating them. We also observed that for low densities, the polarization velocity shows a non-Gaussian behavior with heavy tails associated with long-range correlation and becomes Gaussian for high densities, presenting an uncorrelated regime.

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Acknowledgements

This work was supported by CAPES (Coordenação de Aper-feiçoamento de Pessoal de Nível Superior), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) and FACEPE (Fundação de Amparo à Ciência e Tecnologia do Estado de Pernambuco).

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Authors and Affiliations

  1. Departamento de Física, Universidade Federal Rural de Pernambuco, Rua Manoel de Medeiros, s/n - Dois Irmãos, Recife, 52171-900, Brazil

    Antonio R. de C. Romaguera, João V. A. Vasconcelos, Luis G. Negreiros-Neto, Adauto J. F. de Souza, Viviane M. de Oliveira & Anderson L. R. Barbosa

  2. Centro de Apoio à Pesquisa, Universidade Federal Rural de Pernambuco, Rua Manoel de Medeiros, s/n - Dois Irmãos, Recife, 52171-900, Brazil

    Nathan L. Pessoa

  3. Departamento de Morfologia e Fisiologia Animal, Universidade Federal Rural de Pernambuco, Rua Manoel de Medeiros, s/n - Dois Irmãos, Recife, 52171-900, Brazil

    Jadson F. da Silva & Pabyton G. Cadena

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  1. Antonio R. de C. Romaguera
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  2. João V. A. Vasconcelos
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  8. Viviane M. de Oliveira
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Contributions

A. R. de C. Romaguera conceived the experimental procedure, analyzed the data, and wrote the manuscript. J. V. A. Vasconcelos and Luis G. Negreiros-Neto conducted the experiments and analyzed the data. N. L. Pessoa analyzed the data and contributed to manuscript writing. J. F. da Silva and P. G. Cadena provided the animals and oversaw the ethical committee for experiments involving living animals. Adauto J. F. de Souza, Viviane M. de Oliveira, and Anderson L. R. Barbosa analyzed the data and contributed to manuscript writing.

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Correspondence to Antonio R. de C. Romaguera.

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Romaguera, A.R.d.C., Vasconcelos, J.V.A., Negreiros-Neto, L.G. et al. Multifractal fluctuations in zebrafish (Danio rerio) polarization time series. Eur. Phys. J. E 47, 29 (2024). https://doi.org/10.1140/epje/s10189-024-00423-w

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