Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780429972195
Author: Steven H. Strogatz
Publisher: Taylor & Francis
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Chapter 10.3, Problem 12E
Interpretation Introduction

Interpretation:

Let Rn denote the value of r at which the logistic map has a superstable cycle of the period 2n.

  • a) To write an implicit, but exact, formula for Rn in terms of the point x =12 and the function f(x,r) = rx(1-x).

  • b) To find R2,R3........,R7 to five significant figures using computer and result of part a).

  • c) To find R6R5R7R6.

Concept Introduction:

  • ➢ The periodic orbit has a period p and the fixed point is the intersection point between the line and function which is not greater than the period of the orbit.

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3. Consider the following theorem: Theorem: If n is an odd integer, then n³ is an odd integer. Note: There is an implicit universal quantifier for this theorem. Technically we could write: For all integers n, if n is an odd integer, then n³ is an odd integer. (a) Explore the statement by constructing at least three examples that satisfy the hypothesis, one of which uses a negative value. Verify the conclusion is true for each example. You do not need to write your examples formally, but your work should be easy to follow. (b) Pick one of your examples from part (a) and complete the following sentence frame: One example that verifies the theorem is when n = We see the hypothesis is true because and the conclusion is true because (c) Use the definition of odd to construct a know-show table that outlines the proof of the theorem. You do not need to write a proof at this time.
matrix 4
Please ensure that all parts of the question are answered thoroughly and clearly. Include a diagram to help explain answers. Make sure the explanation is easy to follow. Would appreciate work done written on paper. Thank you.
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