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Title

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

AuthorsHernández-García, Emilio ; López, Cristóbal
Keywords[PACS] Complex systems: Patterns
[PACS] Population dynamics and ecological pattern formation
[PACS] Fluctuation phenomena, random processes, noise, and Brownian motion
[PACS] Pattern selection; pattern formation
Issue Date30-Jul-2004
PublisherAmerican Physical Society
CitationPhysical Review E 70: 016216 (2004)
AbstractWe introduce a simple model of population dynamics which considers reproducing individuals or particles with birth and death rates depending on the number of other individuals in their neighborhood. The model shows an inhomogeneous quasistationary pattern with many different clusters of particles arranged periodically in space. 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 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, such as the average number of individuals.
Description11 pages, 11 figures.-- PACS nrs.: 89.75.Kd, 87.23.Cc, 05.40.−a, 47.54.+r.-- ArXiv pre-print available at: http://arxiv.org/abs/cond-mat/0310384
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevE.70.016216
URIhttp://hdl.handle.net/10261/7512
DOI10.1103/PhysRevE.70.016216
ISSN1539-3755
Appears in Collections:(IFISC) Artículos
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