I know someone has given me resources for this before but I can't seem to find them... Would someone please summarize stable vs unstable, attracting vs repelling, and node, saddle,etc fixed points? I am getting confused about classifying the fixed points because the information in my book is kind of spread all over, not compiled in a table or something. Thanks, I really appreciate it.
2026-03-27 19:30:08.1774639808
Fixed Point Summary
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We have two type of stable fixed point: asymptotically stable and naturally stable.If the fixed is none of them it's an unstable. x is a naturally stable equilibrium (or fixedpoint) if for every neighborhood U of x there is a neighborhood V⊆U of x such that every solution x(t) starting in V (x(0)∈V) remains in U for all t≥0. Notice that x(t) need not approach x.