Analyze the models for competition between two species given in Problems, using the following outline.
(a) Find and plot the equilibrium points and nullclines. Determine the directions of the vector fields between the nullclines.
(b) Decide whether the equilibrium points are unstable (repelling at least some nearby solutions) or stable (repelling no nearby solutions).
(c) Sketch portions of solution curves near equilibrium points: then complete the phase p malt of the system.
(d) Decide whether the two species described by the model can coexist. What conditions are required for coexistence when it is possible?
dx/dt = x(4 - 2x - y)
dy/dt = y(4 - x - 2y)