Figure 11: When t_c2, t_s2 ≪ t_c1, the timescale t_c1 is characteristic of the time it takes ṗ to reach its maximum, and the timescale $t_{c_1}^{\ast }$ is the approximate time it takes c₂ to reach its maximum, respectively, in the auxiliary reaction mechanism (47)–(48).

The thick black curve is the numerically-integrated solution to the mass action equations (49a)–(49d). The leftmost dashed vertical line corresponds to t_c1, and the rightmost dashed vertical line corresponds to $t_{c_1}^{\ast }=-t_{c_1}\text{ln}{t}_{c_1}∕t_{s_1}$. The lower dotted horizontal line corresponds to the scaled characteristic value $\ell s_2^{\lambda }$. The constants (without units) used in the numerical simulation are: $e_1^0=1$, $s_1^0=100$, $e_2^0=100$, k₁ = 0.01, k₂ = 1, k₃ = 10, k₋₃ = 1, k₄ = 100 and k₋₁ = 1. Time has been mapped to the t_∞ scale: t_∞(t) = 1 – 1/ln[t + exp(1)], and c₂ has been numerically scaled by its maximum value.