Critical dynamic approach to stationary states in complex systems |
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Authors: | A F Rozenfeld K Laneri E V Albano |
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Institution: | (1) Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, INIFTA, UNLP, CONICET, Sucursal 4, Casilla de Correo 16, (1900), La Plata, Argentina |
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Abstract: | A dynamic scaling Ansatz for the approach to stationary states in complex systems
is proposed and tested by means of extensive simulations applied to both
the Bak-Sneppen (BS) model, which exhibits robust Self-Organised
Critical (SOC) behaviour, and the Game of Life (GOL) of J. Conway,
whose critical behaviour is under debate. Considering the dynamic scaling behaviour of the density of
sites (ρ(t)), it is shown that i) by starting the dynamic measurements with configurations
such that ρ(t=0) →0, one observes an initial increase of the
density with exponents θ= 0.12(2) and θ= 0.11(2) for the BS and GOL models, respectively;
ii) by using initial configurations with ρ(t=0) →1, the density decays with exponents δ= 0.47(2) and δ= 0.28(2) for the BS
and GOL models, respectively.
It is also shown that the temporal autocorrelation decays with exponents
Ca = 0.35(2) (Ca = 0.35(5)) for the BS (GOL) model.
By using these dynamically determined critical exponents
and suitable scaling relationships, we also obtain the dynamic
exponents z = 2.10(5) (z = 2.10(5)) for the
BS (GOL) model.
Based on this evidence we conclude that the dynamic
approach to stationary states of the investigated models
can be described by suitable power-law functions
of time with well-defined exponents. |
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Keywords: | |
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