Solved: Consider the system dx/dt = x(a x y), dy/dt = y(c + x), where a, , , c, and are

Chapter 9, Problem 12

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Consider the system dx/dt = x(a x y), dy/dt = y(c + x), where a, , , c, and are positive constants. (a) Find all critical points of the given system. How does their location change as increases from zero? Assume that a/ > c/ , that is, < a/c. Why is this assumption necessary? (b) Determine the nature and stability characteristics of each critical point. (c) Show that there is a value of between zero and a/c where the critical point in the interior of the first quadrant changes from a spiral point to a node. (d) Describe the effect on the two populations as increases from zero to a/c.