Open AccessCollective behavior of coupled multiplicative processes with stochastic resetting
Author(s) -
Ignacio T. Gómez Garay,
Damián H. Zanette
Publication year - 2021
Publication title -
journal of physics. complexity
Language(s) - English
Resource type - Journals
ISSN - 2632-072X
DOI - 10.1088/2632-072x/ac2070
Subject(s) - multiplicative function , statistical physics , coupling (piping) , reset (finance) , stochastic process , variable (mathematics) , gravitational singularity , power law , mathematics , distribution (mathematics) , physics , mathematical analysis , statistics , economics , engineering , mechanical engineering , financial economics
A dynamical variable driven by the combination of a deterministic multiplicative process with stochastic reset events develops, at long times, a stationary power-law distribution. Here, we analyze how such distribution changes when several variables of the same kind interact with each other through diffusion-like coupling. While for weak coupling the variables are still distributed following power-law functions, their distributions are severely distorted as interactions become stronger, with sudden appearance of cutoffs and divergent singularities. We explore these effects both analytically and numerically, for coupled ensembles of identical and non-identical variables. The most relevant consequences of ensemble heterogeneity are assessed, and preliminary results for spatially distributed ensembles are presented.