Lattice Lotka-Volterra model with long range mixing

A spatio-temporal process in the Lattice Lotka Volterra (LLV) model, when realized on low dimensional support, is studied. It is shown that the introduction of a long-range mixing causes a drastic change in the system’s behavior, which transits from small random-like fluctuations to global oscillations when the mixing rate transcends above a critical point. The amplitude of the induced oscillations is well defined by the mixing rate and is insensitive to the initial conditions and the lattice size variations. The observed behavior essentially differs from that predicted by the Mean-Field model which is conservative. The oscillations are of limit-cycle type and appear as a stochastic analog of a Hopf bifurcation.