Consider the system x = x(1 x 0.5y), y = y(0.75 + 0.25x), (25) where > 0. Observe that

Chapter 9, Problem 11

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Consider the system x = x(1 x 0.5y), y = y(0.75 + 0.25x), (25) where > 0. Observe that this system is a modification of the system (2) in Example 1. (a) Find all of the critical points. How does their location change as increases from zero? Observe that there is a critical point in the interior of the first quadrant only if < 1/3. (b) Determine the type and stability property of each critical point. Find the value 1 < 1/3 where the nature of the critical point in the interior of the first quadrant changes. Describe the change that takes place in this critical point as passes through 1. (c) Draw a direction field and phase portrait for a value of between zero and 1; for avalue of between 1 and 1/3.(d) Describe the effect on the two populations as increases from zero to 1/3.