Abstract
Birth-death processes often exhibit an oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable on the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey interaction. Fluctuation effects due to discreteness of the populations destroy the mean-field stability and eventually drive the system toward extinction of one or both species. We show that the corresponding extinction time scales as a certain power-law of the population sizes. This behavior should be contrasted with the extinction of models stable in the mean-field approximation. In the latter case the extinction time scales exponentially with size.
Original language | English (US) |
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Article number | 021129 |
Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |
Volume | 80 |
Issue number | 2 |
DOIs | |
State | Published - Aug 27 2009 |