  We introduce a model of three-species two-particle diffusion-limited
reactions A+B -> A or B, B+C -> B or C, and C+A -> C or A, with three
persistence parameters (survival probabilities in reaction) of the hopping
particle. We consider isotropic and anisotropic diffusion (hopping with a
drift) in 1d. We find that the particle density decays as a power-law for
certain choices of the persistence parameter values. In the anisotropic case,
on one symmetric line in the parameter space, the decay exponent is
monotonically varying between the values close to 1/3 and 1/2. On another, less
symmetric line, the exponent is constant. For most parameter values, the
density does not follow a power-law. We also calculated various characteristic
exponents for the distance of nearest particles and domain structure. Our
results support the recently proposed possibility that 1d diffusion-limited
reactions with a drift do not fall within a limited number of distinct
universality classes.
