Digging deeper, we note that an analytical solution to (54a) is given in terms of a Lambert-W function Fig. The inner solution (54a) (dashed red curve) provides a good approximation to the mass action equations ( )-(7d) (solid black curve) when t ≤ ts 2 , while the outer solution (54b) (dashed blue curve) provides a good approximation when t > ts 2 . Parameter values for numerical solutions are: