Oscillatory behavior in a lattice prey-predator system

Using Monte Carlo simulations we study a lattice model of a prey-predator system. We show that in the three-dimensional model populations of preys and predators exhibit coherent periodic oscillations but such a behavior is absent in lower-dimensional models. Finite-size analysis indicate that amplitude of these oscillations is finite even in the thermodynamic limit. This is an example of a microscopic model with stochastic dynamics which exhibits oscillatory behavior without any external driving force. We suggest that oscillations in our model are induced by some kind of stochastic resonance.