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arXiv · 1111.1306

Herding model and 1/f noise

J. Ruseckas·B. Kaulakys·V. Gontis
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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.

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J. Ruseckas, B. Kaulakys, V. Gontis. 2011-11-05. Herding model and 1/f noise. https://doi.org/10.1209/0295-5075%2F96%2F60007

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