One-dimensional generalized branching annihilating random walker process with stochastic generation of offsprings

We introduce a branching annihilating random walker process with two species, particles A and B, which diffuse creating new particles and annihilating instantaneously (A + B → 0) when they meet. Each kind of particle branches stochastically having offsprings of the same or different type. The model is defined and studied by means of epidemic simulations in a one-dimensional discrete lattice. The phase diagram of the model exhibits two states, the vacuum and the active one, separated by a critical line. Along that line the system undergoes irreversible second order phase transitions. Monte Carlo results show that the transitions belong to the same universality class as directed percolation. In the limiting case when the generation of offsprings is forbidden, the model is mapped into the standard diffusion-limited reaction A+B→0 which asymptotically evolves towards the vacuum state. The transition between the stationary regime and such vacuum states is also studied.