Science:Math Exam Resources/Courses/MATH103/April 2013/Question 05 (a)
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Question 05 (a) 

Consider the iterated map . Calculate the steady states (fixedpoints, equilibria) and mark them in the sketch below. Determine the stability of each equilibrium (explain analytically or graphically). Plot a cobweb starting with just above 2 (the point is indicated in the sketch).

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Hint 

Recall in this setting, steady states are found by setting . 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. The steady states are given by solving Subtracting x from both sides yields Using the quadratic formula gives
Analytically to check stability, we would need to take the derivative of our function and then plug in the fixed points and check that the absolute value of the derivatives in the fixed points is less than 1 (this would show that the fixed point is stable). It's easier to notice that graphically, none of the fixed points are the limit of an iterative sequence and so none of the fixed points are stable. 