Temporal correlations in the Vicsek model with vectorial noise

BAGLIETTO, GABRIEL; ROZENFELD, ALEJANDRO F.; GULICH, DAMIÁN

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Lugar: Amsterdam; Año: 2018 vol. 502 p. 590 - 604

0378-4371

We study the temporal correlations in the evolution of the order parameter ϕ(t) 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).