A Yule-Simon process with memory

TL;DR

This paper introduces a modified Yule-Simon model incorporating a hyperbolic memory kernel, which alters the system's growth dynamics and provides new analytical insights into frequency distributions.

Contribution

It presents a novel Yule-Simon model with memory effects, offering analytical solutions for distribution densities and rank distributions.

Findings

Memory kernel significantly affects attachment properties

Derived approximate analytical solutions

Altered frequency and rank distribution behaviors

Abstract

The Yule-Simon model has been used as a tool to describe the growth of diverse systems, acquiring a paradigmatic character in many fields of research. Here we study a modified Yule-Simon model that takes into account the full history of the system by means of an hyperbolic memory kernel. We show how the memory kernel changes the properties of preferential attachment and provide an approximate analytical solution for the frequency distribution density as well as for the frequency-rank distribution.