(a) To find and classify all the fixed points of the given system. (b) To show that if E is large enough, then the system has a periodic solution on the torus and also to find what kind of bifurcations create periodic solutions. (c) To find the bifurcation curve in (E, K) the space at which these periodic solutions are created. Concept Introduction: ➢ The fixed point of a differential equation is the point where f(x) = 0 ; while substitution f(x) = x ˙ is used and x&*#x00A0;is a fixed point . ➢ The bifurcation curve shows the values approached asymptotically as a function of the system parameters.

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Answer 1

Question

Chapter 8.6, Problem 4E

Interpretation Introduction

Interpretation:

(a) To find and classify all the fixed points of the given system.

(b) To show that if E is large enough, then the system has a periodic solution on the torus and also to find what kind of bifurcations create periodic solutions.

(c) To find the bifurcation curve in (E, K) the space at which these periodic solutions are created.

Concept Introduction:

➢ The fixed point of a differential equation is the point where f(x) = 0 ; while substitution f(x) = x˙ is used and x&*#x00A0;is a fixed point.

➢ The bifurcation curve shows the values approached asymptotically as a function of the system parameters.

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Answer 2

Question

Chapter 8.6, Problem 4E

Interpretation Introduction

Interpretation:

(a) To find and classify all the fixed points of the given system.

(b) To show that if E is large enough, then the system has a periodic solution on the torus and also to find what kind of bifurcations create periodic solutions.

(c) To find the bifurcation curve in (E, K) the space at which these periodic solutions are created.

Concept Introduction:

➢ The fixed point of a differential equation is the point where f(x) = 0 ; while substitution f(x) = x˙ is used and x&*#x00A0;is a fixed point.

➢ The bifurcation curve shows the values approached asymptotically as a function of the system parameters.

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Answer 3

Question

Chapter 8.6, Problem 4E

Interpretation Introduction

Interpretation:

(a) To find and classify all the fixed points of the given system.

(b) To show that if E is large enough, then the system has a periodic solution on the torus and also to find what kind of bifurcations create periodic solutions.

(c) To find the bifurcation curve in (E, K) the space at which these periodic solutions are created.

Concept Introduction:

➢ The fixed point of a differential equation is the point where f(x) = 0 ; while substitution f(x) = x˙ is used and x&*#x00A0;is a fixed point.

➢ The bifurcation curve shows the values approached asymptotically as a function of the system parameters.

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Answer 4

Question

Chapter 8.6, Problem 4E

Interpretation Introduction

Interpretation:

(a) To find and classify all the fixed points of the given system.

(b) To show that if E is large enough, then the system has a periodic solution on the torus and also to find what kind of bifurcations create periodic solutions.

(c) To find the bifurcation curve in (E, K) the space at which these periodic solutions are created.

Concept Introduction:

➢ The fixed point of a differential equation is the point where f(x) = 0 ; while substitution f(x) = x˙ is used and x&*#x00A0;is a fixed point.

➢ The bifurcation curve shows the values approached asymptotically as a function of the system parameters.

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Answer 5

Chapter 8.6, Problem 4E

Interpretation Introduction

Interpretation:

(a) To find and classify all the fixed points of the given system.

(b) To show that if E is large enough, then the system has a periodic solution on the torus and also to find what kind of bifurcations create periodic solutions.

(c) To find the bifurcation curve in (E, K) the space at which these periodic solutions are created.

Concept Introduction:

➢ The fixed point of a differential equation is the point where f(x) = 0 ; while substitution f(x) = x˙ is used and x&*#x00A0;is a fixed point.

➢ The bifurcation curve shows the values approached asymptotically as a function of the system parameters.

Answer 6

Chapter 8.6, Problem 4E

Interpretation Introduction

Interpretation:

(a) To find and classify all the fixed points of the given system.

(b) To show that if E is large enough, then the system has a periodic solution on the torus and also to find what kind of bifurcations create periodic solutions.

(c) To find the bifurcation curve in (E, K) the space at which these periodic solutions are created.

Concept Introduction:

➢ The fixed point of a differential equation is the point where f(x) = 0 ; while substitution f(x) = x˙ is used and x&*#x00A0;is a fixed point.

➢ The bifurcation curve shows the values approached asymptotically as a function of the system parameters.

Answer 7

Chapter 8.6, Problem 4E

Interpretation Introduction

Interpretation:

(a) To find and classify all the fixed points of the given system.

(b) To show that if E is large enough, then the system has a periodic solution on the torus and also to find what kind of bifurcations create periodic solutions.

(c) To find the bifurcation curve in (E, K) the space at which these periodic solutions are created.

Concept Introduction:

➢ The fixed point of a differential equation is the point where f(x) = 0 ; while substitution f(x) = x˙ is used and x&*#x00A0;is a fixed point.

➢ The bifurcation curve shows the values approached asymptotically as a function of the system parameters.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Solution Summary: The author explains that the fixed point of a differential equation is the point where f(x*) = 0 and the bifurcation curve shows the values approached asymptotically as

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