8.1: Linearization, Critical Points, and Equilibria ...
https://math.libretexts.org/Bookshelves/Differential_Equations/Book...04.07.2021 · Let us define the critical points as the points (x, y) such that [ f(x, y) g(x, y)] = →0. In other words, the points where both f(x, y) = 0 and g(x, y) = 0. The critical points are where the behavior of the system is in some sense the most complicated. If [f ( x, y) g ( x, y)] is zero, then nearby, the vector can point in any direction whatsoever.