For a equilibrium position $x_0$ and a perturbed (or with error) one $x_0^\prime:= x_0 + \epsilon_0$. Their distance after time $t$ is $\epsilon_t \approx \epsilon_0 e^{t \lambda(x_0)}$. Can I say that the smaller the $\lambda(x_0)$, the "better" its stability is?
For example, it is obviously that for $\lambda=-2$, $\epsilon_t \approx \epsilon_0 e^{t \lambda}$ will converge to $0$ faster, compared to the $\lambda=-1$ case.
Thanks in advance.