Extinction in the Lotka-Volterra model.

@article{Parker2009ExtinctionIT,
  title={Extinction in the Lotka-Volterra model.},
  author={Matthew Parker and Alex Kamenev},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  year={2009},
  volume={80 2 Pt 1},
  pages={021129}
}
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… CONTINUE READING
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