Nullcline

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Nullclines are encountered in two-dimensional systems of differential equations

x' = F (x, y)

y' = G (x, y).

They are curves along which the vector field is either completely horizontal or vertical. Therefore, a nullcline can be the boundary between regions where $x'$ or $y'$ is positive and negative. Nullclines can be found by setting either $x' = 0$ or $y' = 0$ . The intersections between $x$ and $y$ nullclines are equilibrium points, and thus finding nullclines can be a useful way to identify such points, particularly when the system is not amenable to analytical solutions.