  Different branching and annihilating random walk models are investigated by
cluster mean-field method and simulations in one and two dimensions. In case of
the A -> 2A, 2A -> 0 model the cluster mean-field approximations show diffusion
dependence in the phase diagram as was found recently by non-perturbative
renormalization group method (L. Canet et al., cond-mat/0403423). The same type
of survey for the A -> 2A, 4A -> 0 model results in a reentrant phase diagram,
similar to that of 2A -> 3A, 4A -> 0 model (G. \'Odor, PRE {\bf 69}, 036112
(2004)). Simulations of the A -> 2A, 4A -> 0 model in one and two dimensions
confirm the presence of both the directed percolation transitions at finite
branching rates and the mean-field transition at zero branching rate. In two
dimensions the directed percolation transition disappears for strong diffusion
rates. These results disagree with the predictions of the perturbative
renormalization group method.
