Reaction-rate elasticity (source code)

= Reaction-rate elasticity
{title2=$H_{ij}=\partial_{\log\mu_j}\log v_i^- -\partial_{\log\mu_j}\log v_i^+$}

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