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.
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?
Tuesday, September 27, 2011
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.