title: Pattern formation and nonlocal logistic growth.
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.
authors.affiliation: Department of Physics, Bar-Ilan University, Ramat-Gan 52900, Israel.
authors.forename: Nadav M
authors.initials: NM
authors.lastname: Shnerb
mesh_terms: D000818:Animals; D005075:Biological Evolution; D003163:Competitive Behavior / Q000502:physiology*; D003198:Computer Simulation; D006801:Humans; D016015:Logistic Models; D008954:Models, Biological; D010363:Pattern Recognition, Automated; D011158:Population Growth; D011235:Predatory Behavior / Q000502:physiology*; D012641:Selection, Genetic