2D Differential Equation Grapher

This simulator lets you experiment with a two-dimensional constant-coefficient ordinary differential equation system.

You can click an example case from the list, or enter a custom equation, and the vector field will be graphed below. This is not a phase portrait; the arrow lengths accurately represent the velocity. The dashed green lines are the eigenvectors. Click on the graph to place a ball and it will follow the differential equation, leaving a trail behind to show the trajectory!

EigenvaluesCritical Point (0,0)Stability
0 < λ1 < λ2NodeUnstable
λ1 < λ2 < 0NodeAsymptotically stable
λ1 < 0 < λ2Saddle PointUnstable
0 < λ1 = λ2Proper or improper nodeUnstable
λ1 = λ2 < 0Proper or improper nodeAsymptotically stable
λ1, λ2 = (0 < λ) ± iμSpiral PointUnstable
λ1, λ2 = (λ < 0) ± iμSpiral PointAsymptotically stable
λ1 = iμ, λ2 = -iμCenterStable

Equation Type


λ1  ξ1
λ2  ξ2