Consider the equations describing the interactions of robins r and worms w,
dw/dt = w - wr, and dr/dt = -r + rw.
(a) What are the (non-zero) nullclines for this system?
(b) Your nullclines divide the phase plane into four regions. Give a sample point in each region, and indicate for that point whether each of the populations is increasing or decreasing (by entering the word increasing or decreasing appropriate blank):
(i) (w, r) = ( , ) is in one region, where
the population of worms, w is
and the population of robins, r is
(ii) (w, r) = ( , ) is in a second region, where
the population of worms, w is
and the population of robins, r is
(iii) (w, r) = ( , ) is in a third region, where
the population of worms, w is
and the population of robins, r is
(iv) (w, r) = ( , ) is in the fourth region, where
the population of worms, w is
and the population of robins, r is
Notice what your conclusions about these four regions say about how the populations change with time.