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

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