Fig. 10:

ODE model calculations for various branching rates k_b and various (a,b) constant source rates S₁₀ and (c) time-varying source rates. (a) Colored curves show B_s(t_gel), blue dashed lines show its scaling behaviors, and black curves show approximate B_s(t_gel) from Eq. 3.10 using r_ss values computed by solving Eq. 3.5 numerically; (b) Colored curves show average functionality f^A = R_s/M₀₀ at t_gel. In (a) and (b), S₁₀ decreases from 10⁵ (deep red curve) to 10⁻⁵ (deep blue curve). Dashed blue line in (b) and (c) is 2/(1 − B_s/R_s) ≈ 2.7093 (see text). (c) Average functionality for time-varying source rate S₁₀(t) = m₀λ exp(−λt) m₀ = 4 and λ decreases from 10⁵ (deep red curve) to 10⁻⁵ (deep blue curve). Branching rates k_b vary as indicated.