Nonequilibrium phase transition in a lattice prey–predator system

We study a lattice model of a prey–predator system. Mean-field approximation predicts that the active phase, i.e., one with a finite fraction of preys and predators, is a generic phase of this model. Moreover, within this approximation the model exhibits quasi-oscillations resembling Lotka–Volterra systems. However, Monte Carlo simulations for a one-, two-, and three-dimensional versions of this model do not support this scenario and predict that at a certain value of some parameter the model enters the absorbing state, i.e., a state where the entire population of predators dies out and the model is invaded by preys. Simulations for the one-dimensional version indicate that the transition into the absorbing state belongs to the directed percolation universality class.