Time-dependent evolution of the average ratio of HC₃N/N₂H⁺ and the average fractional abundance of HC₃N and N₂H⁺ with respect to H₂ within four different ranges (7 × 10³ AU, 10⁴ AU, 5 × 10⁴ AU, and 10⁵ AU) around the center using model 4 (left panels) and model 6 (right panels). The four evolutionary stages are labeled in each panel, and the observations are also plotted, with the dashed lines as the median values and the dotted lines as the maximums or minimums of observations. The evolution before 10⁴ yr is excluded to show the changes in different stages more clearly. The results within 7 × 10³ AU and 10⁴ AU during the HMSC stage in model 4 completely overlap because of the large r_in > 10⁴ AU.