Pattern formation and nonlocal logistic growth

TL;DR

This paper investigates how nonlocal interactions influence pattern formation in one-dimensional logistic growth models, revealing spontaneous symmetry breaking, bifurcation regimes, and soliton domain walls, supported by analytical and numerical methods.

Contribution

It introduces a detailed analysis of pattern formation in nonlocal logistic growth, identifying bifurcation regimes and deriving soliton solutions for domain walls, advancing understanding of nonlocal interaction effects.

Findings

Spontaneous breakdown of translational invariance occurs at certain parameters.

Bifurcation regimes depend on interaction range.

Domain walls are described as soliton solutions.

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.