Thomas Gilbert

Title: The stochastic Lotka-Volterra predator-prey model: it keeps cycling on!

Abstract: The marginal stability of the oscillations exhibited by the Lotka-Volterra rate equations has been blamed for the apparent failure of stochastic predator-prey dynamics to replicate a stationary regime of stable oscillations; either of the prey or predator populations typically go extinct after a finite time. I will show that a simple modification of the master equation which adequately accounts for the conservation law underlying the rate equations is sufficient to prevent extinction. In the large system-size limit, the observed regime of oscillations is distributed according to the canonical equilibrium distribution of the thermostatted rate equations.