Pattern formation and nonlocal logistic growth

Details Pattern formation and nonlocal logistic growth Pattern formation and nonlocal logistic growth

2003-11-11

arxiv.org/abs/cond-mat/0311230v2

Physics

Condensed Matter

Soft Condensed Matter

Scientific paper

10.1103/PhysRevE.69.061917

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.

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