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 $A\overrightarrow{A}\varnothing ,$ $B\overrightarrow{B}\varnothing ,$ explicit particle diffusion, and binary pair production processes compete with each other. Several versions with spatially different production are explored, and it is shown that for the cases $2\overrightarrow{A}3A,$ $2\overrightarrow{B}3B$ and $2\overrightarrow{A}2AB,$ $2\overrightarrow{B}2BA$ a phase transition occurs at zero production rate $(\sigma =0),$ which belongs to the class of N-component, asymmetric branching and annihilating random walks, characterized by the order parameter exponent $\beta =2.\mathrm{}$ In the model with particle production $A\overrightarrow{B}ABA,$ $B\overrightarrow{A}\mathrm{BAB}$ a phase transition point can be located at ${\sigma }_c=0.3253\mathrm{}$ which belongs to the class of one-component binary spreading processes.