Exercise 2.3 - Wizzles and Woozles

This is exercise 3.3 from the text, which is 2.2 online, and 2.3 in my nomenclature.

1. Consider a population of wizzles, which unlike woozles can multiply only when their numbers are larger than a certain minimal value a. If there are less byukies than a, they cannot find a partner for mating and the population dies off. The carrying capacity of the island where wizzles live is also A. Obviously A > a. What model would describe the population dynamics of wizzles on this island?

2. What are the equilibria in the byukies model? Are they stable? 

The solution that comes to mind isn't very satisfying, but it works. I've added an IF statement to the growth rate, such that if the A > a, the growth rate is positive, and if A < a, the growth rate is negative. The first image shows the model still works when the Ao > a; the second image shows the stable equilibrium at zero if the Ao < a.