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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?

Thanks.

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

Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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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