Birth, death and diffusion of interacting particles

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.