q-exponential relaxation of the expected avalanche size in the coherent noise model

S.-R.G. Christopoulos and N.V. Sarlis

Physica A: Statistical Mechanics and its Applications, 2014, vol. 407, issue C, 216-225

Abstract: Recently (Sarlis and Christopoulos (2012)) the threshold distribution function pthres(k)(x) of the coherent noise model for infinite number of agents after the k-th avalanche has been studied as a function of k, and hence natural time. An analytic expression of the expectation value E(Sk+1) for the size Sk+1 of the next avalanche has been obtained in the case that the coherent stresses are exponentially distributed with an average value σ. Here, by using a statistical ensemble of initially identical systems, we investigate the relaxation of the average 〈E(Sk+1)〉 versus k. For k values smaller than kmax(σ,f), the numerical results indicate that 〈E(Sk+1)〉 collapses to the q-exponential (Tsallis (1988)) as a function of k. For larger k values, the ensemble average can be effectively described by the time average threshold distribution function obtained by Newman and Sneppen (1996). An estimate k0(σ,f)(>kmax(σ,f)) of this transition is provided. This ensemble of coherent noise models may be considered as a simple prototype following q-exponential relaxation. The resulting q-values are compatible with those reported in the literature for the coherent noise model.

Keywords: q-exponential; Coherent noise model; Natural time; Off-equilibrium dynamics (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:407:y:2014:i:c:p:216-225

DOI: 10.1016/j.physa.2014.03.090

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