0.0 0.2 0.4 0.6 0.8 1.0 1E-7 1E-6 1E-5 1E-4 1E-3 0.01 0.1 1 0.0 0.2 0.4 0.6 0.8 1.0 b ) a ) q  = 10 e  = 3.00, L  = 50 e  = 0.05, L  = 10 q  = 30 q  = 5 q  = 10 q  = 30 q  = 5 < S  > /  A q  = 30 q  = 10 q  = 5 q  = 10 q  = 30 q  = 5 <  S  > /  A r FIG. 4: Dependence of the final absorbing state with respect to different noise levels and different values of q . In solid line it is included the case with ϵ = 3.00 while dashed lines are the cases with ϵ = 0.05. In black circles are reported the final absorbing states calculated with a network size of L = 50, while in white triangles the case with L = 10. a) Calculation done including one-step neighbors (von Neumann neighborhood). b) Calculation done including two-step neighbors. = 10. Quantitative differences arise only for q = 10 and 30, for ϵ = 0.05 (white triangles in Fig. 4 a)). In general it is observed that the final absorbing state is stable to the same range of noise independent of the network size. The difference obtained, consisting in the higher values of < S > /A for q = 10 and the higher minimum for q = 30 at r = 0.05 (both for ϵ = 0.05) are due to the lower size of the network ( L = 10). There are no quantitative differences for the other parameters due to the rather trivial case of q = 5 (for any value of ϵ > 0) and for the high value of ϵ used in the solid lines. In Fig. 4 b) we have included the same results of panel a) calculated with L = 50, but now considering two-step neighbors. The results are qualitatively the same for ϵ = 3.00 14