.. _foxes:

Lab5b: Foxes in daisyworld
--------------------------

I) Add foxes to Daisyworld, as specified in
Lab 5 question predators:

b) rabbit and fox deathrates
d) a rate at which foxes eat rabbits

Note that while we've considered Aw and Ab to be non-dimensional
daisy concentrations (fractions of the planet covered).  They could
just as easily be daisies per square km.  In the same way
a fox "area" of 0.1 could be 0.1 foxes per square km, or
1 fox every 10 square km.

II) Use the steady-state version of your equations to come up
with an analytic expression for :math:`A_w`, :math:`A_b`, :math:`A_f` and :math:`A_r` in terms of
a (single) death rate chi and birth rates :math:`\beta_w` = :math:`\beta_b`,
:math:`\beta_f` and :math:`\beta_r`. How broad is the range of initial conditions
that produce this steady state?  What range of death/birth
coefficients yield a steady state where one or both of
rabbits and foxes are not extinct?