  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 preys, 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 a
unusual absorbing state where predators are absent and the lattice is fully
occupied by preys. The critical exponents of the system are found to be
different from that of the Directed Percolation universality class and they are
robust against addition of explicit diffusion.
