Journal
JOURNAL OF MATHEMATICAL BIOLOGY
Volume 41, Issue 1, Pages 1-23Publisher
SPRINGER-VERLAG
DOI: 10.1007/s002850000025
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We propose a simple experiment to study delocalization and extinction in inhomogeneous biological systems. The nonlinear steady state for, say, a bacteria colony living on and near a patch of nutrient or favorable illumination (oasis) in the presence of a drift term (wind) is computed. The bacteria, described by a simple generalization of the Fisher equation, diffuse, divide A --> A + A, die A --> 0, and annihilate A + A --> 0. At high wind velocities all bacteria are blown into an unfavorable region (desert), and the colony dies out. At low velocity a steady state concentration survives near the oasis. In between these two regimes there: is a critical velocity at which bacteria first survive. If the desert supports a small nonzero population, this extinction transition is replaced by a delocalization transition with increasing velocity. Predictions for the behavior asa function of wind velocity are made fur one and two dimensions.
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