Consider the following system of two nonlinear, autonomous differential equations:
(a) Find the equilibria and their types via a linearization.
(b) Sketch a phase portrait on with the nullclines and direction arrows in the regions of the plane created by the nullclines.
(c) Sketch a solution trajectory on the phase plane with and , and sketch a plot of and versus on an open interval continaing .
(d) Sketch a solution trajectory on the phase plane with and , and sketch a plot of and versus on an open interval continaing .
(e) Sketch additional representative solutions on the phase plane.
(f) Describe the long term behavior of solutions.