2003/12/31 by Cristobal Lopez, Crístobal López, Emilio Hernandez-Garcia +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #cond-mat.stat-mech #nlin.PS #q-bio.PE
paper · pdf · doi:10.1016/j.physd.2004.08.016
published as Physica D 199, 223 (2004) · 17 pages, 8 figures, elsart style; To appear in Physica D
arxiv created 2004/07/20 · openalex publication_date 2004/09/14 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
A 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.