Home
About/Contact
Newsletters
Events/Seminars
2020 IPS Conference
Study Materials
Corporate Members
Extinction in cyclic evolutionary models
Alex Kamenev
Department of Physics, University of Minnesota, Minneapolis, Minnesota 55455, USA
Competitive birth-death processes often exhibit oscillatory behavior. We investigate a particular case where the oscillation cycles are marginally stable at the mean-field level. An iconic example of such a system is the Lotka-Volterra model of predator-prey competition. 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 in models stable in the mean-field approximation. In the latter case the extinction time scales exponentially with size.