Given a general autonomous dynamical-system, say of the form: $\mathbf{\dot{x}} = f(\mathbf{x})$, if the right-hand-side is highly nonlinear, doing an analysis of fixed points, stability, etc... can become quite complicated. For this reason and potentially others, I was curious if it would be correct/appropriate to work with the Taylor series expansion of the right-hand-side instead?



closed as too broad by parsiad, Claude Leibovici, Lord Shark the Unknown, Alex Provost, Cesareo Mar 17 at 8:39

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    $\begingroup$ This is too broad. Perhaps give a particular system and ask a specific question (e.g., I can prove that this "approximate" system is stable; is the original system stable?). $\endgroup$ – parsiad Mar 17 at 3:57