Nullcline Plot

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A nullcline plot for a system of two nonlinear differential equations provides a quick tool to analyze the long-term behavior of the system. The and nullclines (, ) are shown in red and blue, respectively. The nullclines separate the phase plane into regions in which the vector field points in one of four directions: NE, SE, SW, or NW (indicated here by different shades of gray). The equilibrium points of the system are the points of intersection of the two kinds of nullclines. Hovering over an equilibrium point displays a tooltip with the eigenvalues of the linearization of the system at that point.

Contributed by: Helmut Knaust (December 2013)
Open content licensed under CC BY-NC-SA



Displaying a solution with its initial value at the locator is optional.


[1] P. Blanchard, R. L. Devaney, and G. R. Hall, Differential Equations, 4th ed., Boston: Brooks–Cole, 2010 pp. 478ff.

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