Phase transitions and oscillations in a lattice prey-predator model - art.no. 056119

A coarse grained description of a two-dimensional prey-predator system is g iven in tens of a simple three-state lattice model containing two control p arameters: the spreading rates of prey and predator. The properties of the model are investigated by dynamical mean-field approximations and extensive numerical simulations. It is shown that the stationary state phase diagram is divided into two phases: a pure prey phase and a coexistence phase of p rey and predator in which temporal and spatial oscillations can be present. Besides the usual directed percolationlike transition, the system exhibits an unexpected, different type of transition to the prey absorbing phase. T he passage from the oscillatory domain to the nonoscillatory domain of the coexistence phase is described as a crossover phenomena, which persists eve n in the infinite size limit. The importance of finite size effects are dis cussed, and scaling relations between different quantities are established. Finally, physical arguments, based on the spatial structure of the model, are given to explain the underlying mechanism leading to local and global o scillations.