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.

References in corpus (3)

• Front propagation into unstable states
• Non-local Interaction Effects on Pattern Formation in Population Dynamics
• Reactive glass and vegetation patterns

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