Animated Version of Phase Portrait
A phase portrait is a plot of multiple phase curves corresponding to different initial conditions in the same phase plane.
The solutions to the differential equation are a family of functions.
Graphically, this can be plotted in the phase plane like a two-dimensional vector field.
Vectors representing the derivatives of the points with respect to a parameter (say time t),
that is (dx/dt, dy/dt), at representative points are drawn. With enough of these arrows
in place the system behaviour over the regions of plane in analysis can be visualized and limit cycles can be easily identified.
