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 behaviour is absent
in lower-dimensional models. Finite-size analysis indicate that amplitude of
these oscillations is finite even in the thermodynamic limit. In our opinion,
this is the first example of a microscopic model with stochastic dynamics which
exhibits oscillatory behaviour without any external driving force. We suggest
that oscillations in our model are induced by some kind of stochastic
resonance.Comment: 7 pages, 10 figures, Phys.Rev.E (Nov. 1999
