Consider the equations describing the interactions of robins r and worms w:
dw/dt = w - wr, and dr/dt = -r + rw.
A nullcline for this system is a curve in the w, r phase plane such that either = dw/dt = 0, or dr/dt = 0.
Critical points occur where nullclines intersect. Another application of nullclines is to divide the phase plane into regions where dw/dt and dr/dt are each either positive or negative.
(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.