Solved: In Exercise 9 we considered the problem of predicting the population in a

Chapter 5, Problem 10

(choose chapter or problem)

In Exercise 9 we considered the problem of predicting the population in a predator-prey model. Another problem of this type is concerned with two species competing for the same food supply. If the numbers of species alive at time t are denoted by x1(t) and x2(t), it is often assumed that, although the birth rate of each of the species is simply proportional to the number of species alive at that time, the death rate of each species depends on the population of both species. We will assume that the population of a particular pair of species is described by the equations dx1(t) dt = x1(t)[4 0.0003x1(t) 0.0004x2(t)] and dx2(t) dt = x2(t)[2 0.0002x1(t) 0.0001x2(t)]. If it is known that the initial population of each species is 10,000, find the solution to this system for 0 t 4. Is there a stable solution to this population model? If so, for what values of x1 and x2 is the solution stable?