Spatial instabilities and local oscillations in a lattice gas Lotka–Volterra model

 We analyze the evolution of spatially inhomogeneous perturbations in a lattice gas model for a prey-predator population. Starting with the master equation of the model, decoupled by means of a mean field approximation, spatial instabilities are seen to take place in a region of the phase diagram. This is in qualitative agreement with local oscillations already observed in computer simulations. We determine the transition line that separates the homogeneous region from the inhomogeneous region and we study the spatio-temporal self-organized structures that appear inside the inhomogeneous region.