WinslowQuiz2Key - 1 Consider the map xn 1 = 2xn(1 xn Derive...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1. Consider the map x n+1 = 2x n /(1+x n ) . Derive all fixed points and evaluate their stability. Show your work. Answer : 0 ) 1 ( 1 2 = + = x x x x x simplifies to… Therefore, x = 0 or 1 are the fixed points. Evaluate the first derivative to determine stability, by the quotient rule the derivative is: ( ) 1 , 0 2 1 1 , 0 ) 1 ( * 2 ) 1 ( * 2 = = + + = x x x x x dx x df @ x = 0 , ( ) 2 = dx x df @ x = 1 , ( ) 5 . 0 = dx x df Therefore, the fixed point at 0 is unstable and the fixed point at 1 is stable. 2 . For each map below, generate cobweb plots to determine the map’s behavior (ignore ranges of inputs that give you imaginary numbers. Use these plots in order to fully describe all fixed points and their stability. a. x n+1 =sqrt(x n ) Answer
Image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon