Question

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?

Answer 1

yes, the model gives a realistic behavior

Step-by-step explanation:

This describes the inner equilibrium point is a stable node, here it's a center. These are periodic solutions. Populations of the mice and owls are periodic. It describes: when the mice population is lower, the owl population decreases; again the owl is lower so mice got a chance to grow its population; now as sufficient food(mice) is there, the owl population increases; as predator population increases, the prey population decreases; and this continues as a cycle forever.

So, yes, the model gives a realistic behavior.

Check attachment