First, write some words to explain why these equations make sense. Then, fix , (it's notorius that rabbits have the tendency to reproduce quickly) and . For a few initial conditions of your choice, plot the trajectories in the -plane (say, with and ). For the same initial conditions, plot the actual solutions too (i.e, against , and against ). Write some comments interpreting how the behaviour of the solutions relates to what happens to the two species.
Finally, repeat the same procedure with . Things change substantially. Again, what is the ``physical'' interpretation of this?