Let R n denote the value of r at which the logistic map has a superstable cycle of the period 2 n . a) To write an implicit, but exact, formula for R n in terms of the point x = 1 2 and the function f ( x,r ) = rx ( 1-x ) . b) To find R 2 ,R 3 ........ ,R 7 to five significant figures using computer and result of part a). c) To find R 6 − R 5 R 7 − R 6 . 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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Answer 1

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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 R6−R5R7−R6.

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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Answer 2

Question

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 R6−R5R7−R6.

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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Answer 3

Question

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 R6−R5R7−R6.

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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Answer 4

Question

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 R6−R5R7−R6.

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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Answer 5

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 R6−R5R7−R6.

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.

Answer 6

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 R6−R5R7−R6.

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.

Answer 7

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 R6−R5R7−R6.

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.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Solution Summary: The author explains that the periodic orbit has a period p and the fixed point is the intersection point between the line and function.

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