Limit cycle or attractor

Description
"Linear phase portraits is classified using the (Tr,Det) plane.
In the (Tr,Det) plane, the stable region is the upper left quadrant.
It is bounded by the straight half-lines where either the eigenvalues
are purely imaginary, or one is zero and the other is negative. Limits of linearization are discussed. If the linearization is not on the borderline of the stable quadrant, it correctly predicts the stability of the equilibrium. The limit cycle is an ""attractor,"" in the sense that every nearby trajectory stays nearby and converges to it. Limit cycles for 2D systems is analysed.
Prof. Arthur Mattuck, Maths, 18.03.Differential Equations, Spring 2010: 31: Limit Cycles: Massachusetts Institute of Technology: MIT Open Course Ware),http://ocw.mit.edu (Accessed December 8, 2011). License: Creative Commons BY-NC-SA: http://ocw.mit.edu/terms/#cc