Question: Two companies share the market for a new technology. They have no competition except each other. Let A(t) be the net worth of one company and B(t) the net worth of the other at time t. Suppose that net worth cannot be negative and that A and B satisfy the differential equations
A' = 2A - AB
B' = B - AB
(a) What do these equations predict about the net worth of each company if the other were not present? What effect do the companies have on each other?
(b) Are there any equilibrium points? If so, what are they?
(c) Sketch a slope field for these equations (using a computer or calculator), and hence describe the different possible long-run behaviors.