Multicomponent binary spreading process

I investigate numerically the phase transitions of two-component generalizations of binary spreading processes in one dimension. In these models pair annihilation: AA->0, BB->0, explicit particle diffusion and binary pair production processes compete with each other. Several versions with spatially different productions have been explored and shown that for the cases: 2A->3A, 2B->3B and 2A->2AB, 2B->2BA a phase transition occurs at zero production rate ($\sigma =0$), that belongs to the class of N-component, asymmetric branching and annihilating random walks, characterized by the order parameter exponent $\beta =2$. In the model with particle production: AB->ABA, BA-> BAB a phase transition point can be located at ${\sigma }_c=0.3253$ that belongs to the class of the one-component binary spreading processes.