Using the phase plane program, plot the phase plane for the Lotka-Volterra model:
x' = (a – by)x
у' = (сх – d)у
Here x(t) represents the population of a prey species, say mice, and y(t) is the population of a predator species, for example, owls. If there are no owls, then the population of mice grows exponentially, and if there are no mice, then the owls die off. However, if the initial populations are both positive, then interesting stuff happens.
Plot the phase plane including a number of solutions of this system with a = b = c = d =1. You decide what is are good limits for your axes. Describe the solutions in a few words.
Do you think that this model gives realistic behavior?