Herding model and 1/f noise

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 earlie...

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Bibliographic Details
Published inarXiv.org
Main Authors Ruseckas, J, Kaulakys, B, Gontis, V
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 05.11.2011
Subjects
Agent-based models
Differential equations
Linearity
Mathematical models
Noise
Nonlinear equations
Nonlinearity
Physics - Adaptation and Self-Organizing Systems
Physics - Data Analysis, Statistics and Probability
Power spectral density
Transition probabilities
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Summary: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.
ISSN:2331-8422
DOI:10.48550/arxiv.1111.1306