To find whether the given diagram is for the parameter h > 0 or h < 0 . Concept Introduction: Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric. Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases. Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

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Answer 1

Question

Chapter 3.6, Problem 1E

Interpretation Introduction

Interpretation:

To find whether the given diagram is for the parameter h > 0 or h < 0.

Concept Introduction:

Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric.

Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases.

Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

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Answer 2

Question

Chapter 3.6, Problem 1E

Interpretation Introduction

Interpretation:

To find whether the given diagram is for the parameter h > 0 or h < 0.

Concept Introduction:

Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric.

Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases.

Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

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Answer 3

Question

Chapter 3.6, Problem 1E

Interpretation Introduction

Interpretation:

To find whether the given diagram is for the parameter h > 0 or h < 0.

Concept Introduction:

Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric.

Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases.

Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

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Answer 4

Question

Chapter 3.6, Problem 1E

Interpretation Introduction

Interpretation:

To find whether the given diagram is for the parameter h > 0 or h < 0.

Concept Introduction:

Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric.

Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases.

Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

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Answer 5

Chapter 3.6, Problem 1E

Interpretation Introduction

Interpretation:

To find whether the given diagram is for the parameter h > 0 or h < 0.

Concept Introduction:

Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric.

Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases.

Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

Answer 6

Chapter 3.6, Problem 1E

Interpretation Introduction

Interpretation:

To find whether the given diagram is for the parameter h > 0 or h < 0.

Concept Introduction:

Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric.

Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases.

Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

Answer 7

Chapter 3.6, Problem 1E

Interpretation Introduction

Interpretation:

To find whether the given diagram is for the parameter h > 0 or h < 0.

Concept Introduction:

Instability parameter is the parameter added in the system which causes the symmetric solution to break, and the solution no longer remains symmetric.

Pitchfork bifurcationis: the bifurcation mainly seen in symmetrical physical problems. Stable or unstable fixed points appear and disappear in pairs in such cases.

Problems in which the pair of unstable symmetric fixed points emerge are called supercritical pitchfork bifurcation.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E

Solution Summary: The author analyzes the effect of the instability parameter on the stability diagram of pitchfork bifurcations.

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