Comments on mathematical aspects of the Bir\'o-N\'eda model
Mathematical Physics
2023-11-23 v1 Statistical Mechanics
math.MP
Adaptation and Self-Organizing Systems
Abstract
We address two mathematical aspects of the Bir\'o--N\'eda dynamical model, recently applied in the statistical analysis of several and varied complex phenomena. First, we show that a given implicit assumption ceases to be valid outside the most simple and common cases, and we analyze the consequences thereof, in what the formulation of the model and probability conservation is concerned. Second, we revisit the transient behavior in the case of a constant reset rate and a constant or linear growth rate, improving on a previous analysis by including more general initial conditions.
Keywords
Cite
@article{arxiv.2311.13449,
title = {Comments on mathematical aspects of the Bir\'o-N\'eda model},
author = {Ilda Inácio and José Velhinho},
journal= {arXiv preprint arXiv:2311.13449},
year = {2023}
}