diff --git a/docs/src/introduction_to_catalyst/math_models_intro.md b/docs/src/introduction_to_catalyst/math_models_intro.md index 1357178f56..0a2647a799 100644 --- a/docs/src/introduction_to_catalyst/math_models_intro.md +++ b/docs/src/introduction_to_catalyst/math_models_intro.md @@ -28,11 +28,11 @@ with $\alpha^k = (\alpha_1^k,\dots,\alpha_M^k)$ its substrate stoichiometry vect As explained in [the Catalyst introduction](@ref introduction_to_catalyst), for a mass action reaction where the preceding reaction has a fixed rate constant, $k$, this function would be the rate law ```math -a_k(\mathbf{X}(t)) = k \prod_{m=1}^M \frac{(X_m(t))^{\sigma_m^k}}{\sigma_m^k!}, +a_k(\mathbf{X}(t)) = k \prod_{m=1}^M \frac{(X_m(t))^{\alpha_m^k}}{\alpha_m^k!}, ``` for RRE ODE and CLE SDE models, and the propensity function ```math -a_k(\mathbf{X}(t)) = k \prod_{m=1}^M \frac{X_m(t) (X_m(t)-1) \dots (X_m(t)-\sigma_m^k+1)}{\sigma_m^k!}, +a_k(\mathbf{X}(t)) = k \prod_{m=1}^M \frac{X_m(t) (X_m(t)-1) \dots (X_m(t)-\alpha_m^k+1)}{\alpha_m^k!}, ``` for stochastic chemical kinetics jump process models. @@ -41,7 +41,7 @@ For the reaction $2A + B \overset{k}{\to} 3 C$ we would have ```math \mathbf{X}(t) = (A(t), B(t), C(t)) ``` -with $\sigma_1 = 2$, $\sigma_2 = 1$, $\sigma_3 = 0$, $\beta_1 = 0$, $\beta_2 = +with $\alpha_1 = 2$, $\alpha_2 = 1$, $\alpha_3 = 0$, $\beta_1 = 0$, $\beta_2 = 0$, $\beta_3 = 3$, $\nu_1 = -2$, $\nu_2 = -1$, and $\nu_3 = 3$. For an ODE/SDE model we would have the rate law ```math