Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates

Details Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates Clustering, advection and patterns in a model of population dynamics with neighborhood-dependent rates

2003-10-16

arxiv.org/abs/cond-mat/0310384v2

Physical Review E 70, 016216 (2004)

Physics

Condensed Matter

Some typos and some problems with the figures corrected

Scientific paper

10.1103/PhysRevE.70.016216

We introduce a simple model of population dynamics which considers birth and death rates for every individual that depend on the number of particles in its neighborhood. The model shows an inhomogeneous quasistationary pattern with many different clusters of particles. We derive the equation for the macroscopic density of particles, perform a linear stability analysis on it, and show that there is a finite-wavelength instability leading to pattern formation. This is the responsible for the approximate periodicity with which the clusters of particles arrange in the microscopic model. In addition, we consider the population when immersed in a fluid medium and analyze the influence of advection on global properties of the model.

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