Eur. Phys. J. B (2014) 87: 169
https://doi.org/10.1140/epjb/e2014-50349-0

Regular Article

Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model

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

^a e-mail: aleksejus.kononovicius@tfai.vu.lt

Received: 14 April 2014
Received in final form: 29 May 2014
Published online: 1 August 2014

Abstract

Systems with long-range interactions often exhibit power-law distributions and can by described by the non-extensive statistical mechanics framework proposed by Tsallis. In this contribution we consider a simple model reproducing continuous transition from the extensive to the non-extensive statistics. The considered model is composed of agents interacting among themselves on a certain network topology. To generate the underlying network we propose a new network formation algorithm, in which the mean degree scales sub-linearly with a number of nodes in the network (the scaling depends on a single parameter). By changing this parameter we are able to continuously transition from short-range to long-range interactions in the agent-based model.