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Two species of fish that compete with each other for food, but do not prey on each
Chapter 9, Problem 6(choose chapter or problem)
Two species of fish that compete with each other for food, but do not prey on each other, are bluegill and redear. Suppose that a pond is stocked with bluegill and redear, and let x and y be the populations of bluegill and redear, respectively, at time t. Suppose further that the competition is modeled by the equations dx dt = x(1 1x 1 y), dy dt = y(2 2 y 2x). a. If 2/2 > 1/1 and 2/2 > 1/1, show that the only equilibrium populations in the pond are no fish, no redear, or no bluegill. What will happen for large t? b. If 1/1 > 2/2 and 1/1 > 2/2, show that the only equilibrium populations in the pond are no fish, no redear, or no bluegill. What will happen for large t?
Questions & Answers
QUESTION:
Two species of fish that compete with each other for food, but do not prey on each other, are bluegill and redear. Suppose that a pond is stocked with bluegill and redear, and let x and y be the populations of bluegill and redear, respectively, at time t. Suppose further that the competition is modeled by the equations dx dt = x(1 1x 1 y), dy dt = y(2 2 y 2x). a. If 2/2 > 1/1 and 2/2 > 1/1, show that the only equilibrium populations in the pond are no fish, no redear, or no bluegill. What will happen for large t? b. If 1/1 > 2/2 and 1/1 > 2/2, show that the only equilibrium populations in the pond are no fish, no redear, or no bluegill. What will happen for large t?
ANSWER:Step 1 of 5
(a) We need to find the critical points.
In order to do that we set 
