Chapter 9.5, Problem 1P

(a)

To determine

To draw: The direction field and to describe its behavior.

(b)

To determine

The critical point.

(c)

To determine

The corresponding linear system, eigen value and eigen vector at each critical point.

(d)

To determine

To sketch: The trajectories in the neighborhood of each critical point.

(e)

To determine

To draw: A phase portrait of given differential system.

(f)

To determine

The limiting behavior of x and y as $t\to \infty$ and interpret the results in terms of the populations of the two species.