Consider the case of rabbits and foxes in Australia. The number of rabbits is x1 and if left alone, it would grow indefinitely (until the food supply was exhausted) so that
x1 = kx1.
However, with foxes present on the continent, we have
x1 = kx1 - ax2,
where x2 is the number of foxes. Now, if the foxes must have rabbits to exist, we have
x2 = -hx2 + bx1.
Determine whether this system is stable and thus decays to the condition x1(t) = x2(t) = 0 at t = ∞. What are the requirements on a, b, h, and k for a stable system? What is the result when k is greater than h?