Phase plane method
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In the context of nonlinear system analysis, the phase plane method refers to graphically determining the existence of limit cycles. The phase plane, applicable for second order systems only, is a plot with axes being the values of the two state variables, x2 vs. x1. Vectors representing the derivatives [f2(x1,x2),f1(x1,x2)] at representative points are drawn. With enough of these arrows in place the system behavior over the entire plane can be visualized and limit cycles can be easily identified.
