Multifractal fluctuations in zebrafish (Danio rerio) polarization time series

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.