  Demographic oscillators are individual-based systems exhibiting temporal
cycles sustained by the stochastic dynamics of the microscopic interacting
particles. We here use the example of coupled predator-prey oscillators to show
that synchronization to a common frequency can occur between two such systems,
even if they oscillate at different frequencies in the absence of coupling. The
power spectra of the separate and the coupled systems are computed within a van
Kampen expansion in the inverse system size, and it is found that they exhibit
two peaks at separate frequencies at low coupling, but that only one peak is
present at large enough coupling strength. We further make predictions on the
time behaviour of the phases of the two oscillators, and their phase
difference, and confirm the frequency entrainment at sufficiently large
coupling. Theoretical results are verified convincingly in numerical
simulations.
