# Keep 'er steady

A dynamical system is described by the equation $$\frac{d}{dt}p = f(p)$$ where $$f(p)$$ 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 ($$\dot{p}(r_i) = 0$$).

Suppose 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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