Saw an interesting mathematical function on populations, showing how it could be normal for a wild population to have seemingly chaotic rises and falls. I thought it'd be pretty easy to adapt the sine function previously posted to this "Verhulst" model:

Try some different growth rates (2.2 seems to work pretty well) to see the population bounce around from year to year.

Right click and download this link to the source if you want to compile it in Flex Builder.