Linear flows

Drag the point on the Trace and determinant pad (the small chart in the corner of the picture follows it): across is the trace, up is the determinant. With a positive determinant, orbits above the parabola turn as they go: a spiral. Below it they do not turn, but all come in, or all go out, along the directions of the two dashed lines: a node. A negative trace draws orbits in, a positive one sends them out, and exactly zero leaves them circling a centre. Once the determinant goes negative, it is a saddle: in along one direction, out along the other.