A limit point. Saddle point A fixed point that has at least one positive eigenvalue and one negative eigenvalue in its linearization. More generally, a fixed point for which there are trajectories that tend to the fixed point in both positive and negative time. Sink A locally asymptotically stable fixed point. Source A fixed point that is unstable and not a saddle-point.
All trajectories move away in positive time.
The set of all points in phase space which are attracted to a fixed point or other invariant orbit in positive time . The branch of solutions occurs for parameter values on the opposite side of the loss of stability. Often indicates that the new branch is unstable. The branch of solutions occurs for parameter values on the same side as the loss of stability. Often indicates that the new branch is stable.