Reaction-rate elasticity ($H_{ij}={\partial }_{\log {\mu }_j}\log v_i^{-}-{\partial }_{\log {\mu }_j}\log v_i^{+}$)

The displayed logarithmic derivative compares the loss and production flux sensitivities of species $i$ to the mean amount ${\mu }_j$. At a steady state $v_i^{+}=v_i^{-}=v_i$, it converts the normalized negative drift Jacobian into $M_{ij}=H_{ij}/{\tau }_i$, where ${\tau }_i={\mu }_i/v_i$ is the mean molecular lifetime. For constant production and loss proportional to ${\mu }^{\alpha }$, the scalar elasticity is $H=\alpha$.

// Target: mathematical-biology.bigb