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Fluctuations impact on a pattern-forming model of population dynamics with non-local interactions

AutorLópez, Cristóbal ; Hernández-García, Emilio
Palabras clavePattern formation
Interacting particle systems
Non-local logistic growth
Fecha de publicación9-ene-2004
CitaciónPhysica D 199(1-2): 223-234 (2004)
ResumenA model of interacting random walkers is presented and shown to give rise to patterns consisting in periodic arrangements of fluctuating particle clusters. The model represents biological individuals that die or reproduce at rates depending on the number of neighbors within a given distance. We evaluate the importance of the discrete and fluctuating character of this particle model on the pattern forming process. To this end, a deterministic mean-field description, including a linear stability and a weakly nonlinear analysis, is given and compared with the particle model. The deterministic approach is shown to reproduce some of the features of the discrete description, in particular, the existence of a finite-wavelength instability. Stochasticity in the particle dynamics, however, has strong effects in other important aspects such as the parameter values at which pattern formation occurs, or the nature of the homogeneous phase.
Descripción12 pages (final published version), 18 pages, 8 figures (attached post-print version).-- ArXiv pre-print available: http://arxiv.org/abs/cond-mat/0312035
Versión del editorhttp://dx.doi.org/10.1016/j.physd.2004.08.016
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