Birth, death and diffusion of interacting particles

TL;DR

This paper investigates a model of diffusing particles with birth-death dynamics influenced by local density, focusing on cluster formation, properties, and the emergence of a single large cluster as interaction distance increases.

Contribution

It introduces a novel analysis of clustering behavior in particle systems with local density-dependent birth dynamics, including the transition to a single cluster at large interaction ranges.

Findings

Clusters have finite lifetime and size depending on parameters

A single large cluster emerges as interaction distance approaches system size

The model characterizes the dynamics of cluster formation and dissolution

Abstract

Individual-based models of chemical or biological dynamics usually consider individual entities diffusing in space and performing a birth-death type dynamics. In this work we study the properties of a model in this class where the birth dynamics is mediated by the local, within a given distance, density of particles. Groups of individuals are formed in the system and in this paper we concentrate on the study of the properties of these clusters (lifetime, size, and collective diffusion). In particular, in the limit of the interaction distance approaching the system size, a unique cluster appears which helps to understand and characterize the clustering dynamics of the model.