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

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.

12 pages, 6 figures

References in corpus (8)

• Statistical mechanics and dynamics of solvable models with long-range interactions
• Network Physiology reveals relations between network topology and physiological function
• Coevolutionary Dynamics: From Finite to Infinite Populations
• Superdiffusion and non-Gaussian statistics in a driven-dissipative 2D dusty plasma
• Coevolutionary dynamics in large, but finite populations
• Stochastic differential equations for evolutionary dynamics with demographic noise and mutations
• Critical Overview of Agent-Based Models for Economics
• Statistics of Lagrangian quantum turbulence

Cited by in corpus (4)

• Spurious memory in non-equilibrium stochastic models of imitative behavior
• Understanding the nature of the long-range memory phenomenon in socioeconomic systems
• Approximation of the first passage time distribution for the birth-death processes
• Hagiotoponyms in France: Saint popularity, like a herding phase transition