We can modify the Lotka-Volterra prey-predator model to include self-limitation of prey: dx = f(x, y) = x (1 - 2/2 - y), dt dy = g(x, y) = y(x 1) - dt where x and y are the population densities of prey and predators (per acre), respectively. (a) Find the three steady states (equilibria) of the system. (b) Fully classify the stability of the three steady states. (Hint: you need to say more than just whether they are stable or unstable). (c) Sketch the phase plane, marking the steady states, the nullclines, and the direction field on the nullclines. (d) Sketch a solution trajectory for some non-zero intial condition, x(0) > 0, y(0) > 0. (e) Describe what happens to the prey and predator populations in the short and long-term for your solution trajectory.