This article creates a pointless content fork with Phase plane, which should explain the method there. Also this article is misleading in saying that:
"to graphically determining the existence of limit cycles" <--- well yes it can determine the rest of the phase portrait especially in linearized systems or linearized approximations (not even stated explicitly), not just non-linear,
"applicable for second order systems only, is a plot with axes being the values of the two state variables, vs. " <--- What does "order" mean to a reader? Also wrong terminology, "order" in this context would refer to the order of the differential equation (e.x. "2nd order linear differential equation" etc.), not to the number of variables. Furthermore an n-order diff eqn can always be reduced to a system of n coupled 1st order eqns. So the terminology used is misleading.
"Vectors representing the derivatives at representative points are drawn." <-- Would be nice to explicitly state that these are derivatives using derivative notation.
"With enough of these arrows in place the system behaviour over the entire plane can be visualized and limit cycles can be easily identified." <-- correct but we could do better, the vectors can be found on the axes, near equilibrium points, on isoclines, none of which is discussed in the article and is essential for actually determining the complete phase in a given region of the phase plane.
I will spill this into phase plane in the next day or so. Maschen (talk) 10:06, 14 September 2012 (UTC)