Consider the systemx= x(1 x 0.5y), y= y(0.75 +

Chapter 9, Problem 11

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Consider the systemx= x(1 x 0.5y), y= y(0.75 + 0.25x),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 value1 < 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