For a more detailed introduction and example problems see http://mathsci2.appstate.edu/~hph/SageMath/
You can evaluate these cells to read about the commands being used in this notebook:






Assume that the number of rabbits grows proportional to the number of rabbits present.
p' = k p


Add a death term  the number of rabbits that die is proportional to the number of 2rabbit interactions.
p' = k p  d p (p1)/2


A different way of thinking about death: The birthrate slows as the population approaches the maximum sustainable in the ecosystem.
p' = k (1  p/M) p

Volterra set the prey (x) increase to simple Malthusean and had the predator (y) affect the prey through the death term. He set the birth term of the predator proportional to both the predators present and the prey present, since predators would have a hard time reproducing without food.
x' = rb * x  rd * x * y
y' = wb * x * y  wd * y


Can you complete these altered predatorprey models? What happens? How are these different from the traditional LV behavior and from each other? Does the behavior make sense?

