Phase plane method
Encyclopedia
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,
vs. 
. Vectors representing the derivative
s
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.
Phase plane
A phase plane is a visual display of certain characteristics of certain kinds of differential equations; it is a 2-dimensional version of the general n-dimensional phase space....
, applicable for second order systems only, is a plot with axes being the values of the two state variables,
vs. . Vectors representing the derivativeDerivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...
s
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.