Modeling1/fnoise

1/fαnoise from self-organized critical models with uniform driving

“…This means that our model can be considered as a physically reasonable generalization of the KM model to systems with a threshold -even if they are spatially extended. As a consequence, the present model combines the idea that 1/f α noise may result from the clustering of the signal pulses [24] with the view that an activation-deactivation process and dissipation are the main features relevant for the description of 1/f α noise [13,16]. The robustness of our results strongly supports these views.…”

“…This is exactly what happens in the KM model for f > γ 3/2 /πσ [24]. To summarize, the crucial ingredient to obtain 1/f noise is the generation of strong enough correlations between different ∆t j such that 1/q k ∆t k obeys the same distribution as ∆t k does.…”

“…Hence, all we need is the probability distribution Ψ of the 1/q q−1 k=0 ∆t k . For the KM model with an average period ∆t, it was shown that Ψ is a Gaussian with mean ∆t and variance σ 2 2γ for f > γ 3/2 /πσ [24]. Hence, 1/q k ∆t k obeys the same distribution as ∆t j and does not depend on q.…”

“…This is indeed the model introduced in Ref. [24]. Kaulakys and Meškauskas (KM) were able to compute analytically the power spectral density and obtained a power law with α = 1.…”

“…This result can be understood to a certain extent by mapping our model to a model introduced by Kaulakys and Meškauskas [24]. In order to do so, we have to neglect all interactions between different sites.…”