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 \(A_w\), \(A_b\), \(A_f\) and \(A_r\) in terms of a (single) death rate chi and birth rates \(\beta_w\) = \(\beta_b\), \(\beta_f\) and \(\beta_r\). 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?