Pattern formation and nonlocal logistic growth
Soft Condensed Matter
2009-11-10 v2 Adaptation and Self-Organizing Systems
Pattern Formation and Solitons
Populations and Evolution
Abstract
Logistic growth process with nonlocal interactions is considered in one dimension. Spontaneous breakdown of translational invariance is shown to take place at some parameter region, and the bifurcation regime is identified for short and long range interactions. Domain walls between regions of different order parameter are expressed as soliton solutions of the reduced dynamics for nearest neighbor interactions. The analytic results are confirmed by numerical simulations.
Cite
@article{arxiv.cond-mat/0311230,
title = {Pattern formation and nonlocal logistic growth},
author = {Nadav M. Shnerb},
journal= {arXiv preprint arXiv:cond-mat/0311230},
year = {2009}
}