$\dot{r} = f(r)$ where $f(r)$ is an $n^\text{th}$ order polynomial with roots $\{r_1,\ldots,r_n\}$. In other words, the roots of $f$ are the steady states of the system ($\dot{r}(r_i) = 0$).

A dynamical system is described by the equationSuppose the system is placed into one of the steady states $r_i$ and is perturbed *very* slightly away to $r_i+\Delta r$. How does the perturbation change over time?

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