Writing , , the linearization of a dynamical system is , . Eliminating gives .
Figure 1.
Contours and descending gradient flow for the 2026 Paper IA 2 potential
. Contour lines of U equal x cubed minus 3x plus open parenthesis x plus 1 close parenthesis y squared are overlaid with the descending gradient field. The highlighted trajectory starts at open parenthesis 2 comma 1 close parenthesis and tends to the local minimum at open parenthesis 1 comma 0 close parenthesis; the other marked critical point is degenerate.

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