Herding model and 1/f noise

Institute of Theoretical Physics and Astronomy, Vilnius University - A. Goštauto 12, LT-01108 Vilnius, Lithuania, EU

^a julius.ruseckas@tfai.vu.lt

Received: 10 August 2011
Accepted: 1 November 2011

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^β noise with different exponents β. 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^β 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.