Abstract
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 as a function of wind velocity are made for one and two dimensions.
Original language | English |
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Pages (from-to) | 1-23 |
Number of pages | 23 |
Journal | Journal of Mathematical Biology |
Volume | 41 |
Issue number | 1 |
DOIs | |
State | Published - Jul 2000 |
Externally published | Yes |
Keywords
- Delocalization
- Disorder
- Extinction
- Fisher equation