  The ecological dynamics of interacting predator and prey populations can
display sustained oscillations, as for instance predicted by the
Rosenzweig-MacArthur predator-prey model. The presence of demographic
stochasticity, due to the finiteness of population sizes, alters the amplitude
and frequency of these oscillations. Here we present a method for
characterizing the effects of demographic stochasticity on the limit cycle
attractor of the Rosenzweig-MacArthur. We show that an angular Brownian motion
well describes the frequency oscillations. In the vicinity of the bifurcation
point, we obtain an analytical approximation for the angular diffusion
constant. This approximation accurately captures the effect of demographic
stochasticity across parameter values.
