= Recovery time of a stable equilibrium
{title2=$\tau=-1/f'(N^*)$}
For a scalar <ordinary differential equation> $N'=f(N)$ and an <equilibrium point> $N^*$ with $f'(N^*)<0$, the <linearization> gives $n'=f'(N^*)n$. Thus small perturbations decay like $e^{-t/\tau}$ with $\tau=-1/f'(N^*)$. This is a local exponential recovery time. In several dimensions, the slowest decaying stable <eigenvalue> typically controls asymptotic recovery, subject to additional polynomial factors for nontrivial <Jordan blocks>.
Back to article page
