Absorbing phase transition in a four-state predator-prey model in one dimension

The model of competition between densities of two different species, called predator and prey, is studied on a one-dimensional periodic lattice, where each site can be in one of the four states, say, empty, or occupied by a single predator, or occupied by a single prey, or by both. Along with the pairwise death of predators and growth of prey, we introduce an interaction where the predators can eat one of the neighboring prey and reproduce a new predator there instantly. The model shows a non-equilibrium phase transition into an unusual absorbing state where predators are absent and the lattice is fully occupied by prey. The critical exponents of the system are found to be different from those of the directed percolation universality class and they are robust against addition of explicit diffusion.