Temporal correlations in the Vicsek model with vectorial noise

Damián Gulich, Gabriel Baglietto and Alejandro F. Rozenfeld

Physica A: Statistical Mechanics and its Applications, 2018, vol. 502, issue C, 590-604

Abstract: We study the temporal correlations in the evolution of the order parameter ϕt for the Vicsek model with vectorial noise by estimating its Hurst exponent H with detrended fluctuation analysis (DFA). We present results on this parameter as a function of noise amplitude η introduced in simulations. We also compare with well known order–disorder phase transition for that same noise range. We find that – regardless of detrending degree – H spikes at the known coexistence noise for phase transition, and that this is due to nonstationarities introduced by the transit of the system between two well defined states with lower exponents. We statistically support this claim by successfully synthesizing equivalent cases derived from a transformed fractional Brownian motion (TfBm).

Keywords: Vicsek model; Self-propelled particles; Scaling range; Fractality; Detrended Fluctuation Analysis; Time series analysis (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:502:y:2018:i:c:p:590-604

DOI: 10.1016/j.physa.2018.02.094

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