Herding model and 1/f noise

Authored by V. Gontis, J. Ruseckas, B. Kaulakys

Date Published: 2011-12

DOI: 10.1209/0295-5075/96/60007

Sponsors: No sponsors listed

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

We provide evidence that for some values of the parameters a simple agent-based model, describing herding behavior, yields signals with 1/f power spectral density. We derive a non-linear stochastic differential equation for the ratio of number of agents and show, that it has the form proposed earlier for modeling of 1/f(beta) noise with different exponents beta. The non-linear terms in the transition probabilities, quantifying the herding behavior, are crucial to the appearance of 1/f noise. Thus, the herding dynamics can be seen as a microscopic explanation of the proposed non-linear stochastic differential equations generating signals with 1/f(beta) spectrum. We also consider the possible feedback of macroscopic state on microscopic transition probabilities strengthening the non-linearity of equations and providing more opportunities in the modeling of processes exhibiting power-law statistics. Copyright (C) EPLA, 2011

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