Diffusion can be included by renormalization of second-order rate constants.
(A) Histograms of monomer frequency for different B values from simulations with Smoldyn software  (first row) and Gillespie simulations of the generalized Schlögl model with (second row) and without (third row) renormalized rate constants of second-order reactions. Standard parameters were used with volume V = 10. The Kullback-Leiber divergence (DKL) shows the closer correspondence of the renormalized reactions than the normal reactions with Smoldyn (forth row). For details on renormalization and calculation of DKL, see Materials and Methods. (B) Corresponding macroscopic bifurcation diagram of deterministic ordinary-differential equation model using renormalized rate constants k±2 to illustrate effect of diffusion. This shows that diffusion delays entry into bistable regime for increasing B.