Degenerate node (${\lambda }_1={\lambda }_2\ne 0$)

A node equilibrium with a repeated nonzero real eigenvalue. If the planar Jacobian matrix has a one-dimensional eigenspace, its linearized solutions contain a term $t{e}^{\lambda t}$ and the node is also called improper. A negative repeated eigenvalue still gives asymptotic stability; a repeated value does not by itself indicate a bifurcation.