Sketch the bifurcation diagram by varying parameter a and summarize the result. Concept Introduction: By changing the parameter, the fixed points move towards each other, collide, and mutually annihilate is known as the saddle node bifurcation. The stabilities of the fixed points interchanged by changing the parameter is known as the transcritical bifurcation. When the single stable fixed point is present and it turns to unstable fixed point due to change in parameter and two new symmetric stable fixed points occur is called supercritical pitchfork bifurcation. When the single unstable fixed point is present and it turns to a stable point due to change in parameter and two new symmetric unstable fixed points occur is called subcritical pitchfork bifurcation.

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Answer 1

Question

Chapter 3.6, Problem 3E

Interpretation Introduction

Interpretation:

Sketch the bifurcation diagram by varying parameter a and summarize the result.

Concept Introduction:

By changing the parameter, the fixed points move towards each other, collide, and mutually annihilate is known as the saddle node bifurcation.

The stabilities of the fixed points interchanged by changing the parameter is known as the transcritical bifurcation.

When the single stable fixed point is present and it turns to unstable fixed point due to change in parameter and two new symmetric stable fixed points occur is called supercritical pitchfork bifurcation.

When the single unstable fixed point is present and it turns to a stable point due to change in parameter and two new symmetric unstable fixed points occur is called subcritical pitchfork bifurcation.

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Answer 2

Question

Chapter 3.6, Problem 3E

Interpretation Introduction

Interpretation:

Sketch the bifurcation diagram by varying parameter a and summarize the result.

Concept Introduction:

By changing the parameter, the fixed points move towards each other, collide, and mutually annihilate is known as the saddle node bifurcation.

The stabilities of the fixed points interchanged by changing the parameter is known as the transcritical bifurcation.

When the single stable fixed point is present and it turns to unstable fixed point due to change in parameter and two new symmetric stable fixed points occur is called supercritical pitchfork bifurcation.

When the single unstable fixed point is present and it turns to a stable point due to change in parameter and two new symmetric unstable fixed points occur is called subcritical pitchfork bifurcation.

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Answer 3

Question

Chapter 3.6, Problem 3E

Interpretation Introduction

Interpretation:

Sketch the bifurcation diagram by varying parameter a and summarize the result.

Concept Introduction:

By changing the parameter, the fixed points move towards each other, collide, and mutually annihilate is known as the saddle node bifurcation.

The stabilities of the fixed points interchanged by changing the parameter is known as the transcritical bifurcation.

When the single stable fixed point is present and it turns to unstable fixed point due to change in parameter and two new symmetric stable fixed points occur is called supercritical pitchfork bifurcation.

When the single unstable fixed point is present and it turns to a stable point due to change in parameter and two new symmetric unstable fixed points occur is called subcritical pitchfork bifurcation.

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Answer 4

Question

Chapter 3.6, Problem 3E

Interpretation Introduction

Interpretation:

Sketch the bifurcation diagram by varying parameter a and summarize the result.

Concept Introduction:

By changing the parameter, the fixed points move towards each other, collide, and mutually annihilate is known as the saddle node bifurcation.

The stabilities of the fixed points interchanged by changing the parameter is known as the transcritical bifurcation.

When the single stable fixed point is present and it turns to unstable fixed point due to change in parameter and two new symmetric stable fixed points occur is called supercritical pitchfork bifurcation.

When the single unstable fixed point is present and it turns to a stable point due to change in parameter and two new symmetric unstable fixed points occur is called subcritical pitchfork bifurcation.

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Answer 5

Chapter 3.6, Problem 3E

Interpretation Introduction

Interpretation:

Sketch the bifurcation diagram by varying parameter a and summarize the result.

Concept Introduction:

By changing the parameter, the fixed points move towards each other, collide, and mutually annihilate is known as the saddle node bifurcation.

The stabilities of the fixed points interchanged by changing the parameter is known as the transcritical bifurcation.

When the single stable fixed point is present and it turns to unstable fixed point due to change in parameter and two new symmetric stable fixed points occur is called supercritical pitchfork bifurcation.

When the single unstable fixed point is present and it turns to a stable point due to change in parameter and two new symmetric unstable fixed points occur is called subcritical pitchfork bifurcation.

Answer 6

Chapter 3.6, Problem 3E

Interpretation Introduction

Interpretation:

Sketch the bifurcation diagram by varying parameter a and summarize the result.

Concept Introduction:

By changing the parameter, the fixed points move towards each other, collide, and mutually annihilate is known as the saddle node bifurcation.

The stabilities of the fixed points interchanged by changing the parameter is known as the transcritical bifurcation.

When the single stable fixed point is present and it turns to unstable fixed point due to change in parameter and two new symmetric stable fixed points occur is called supercritical pitchfork bifurcation.

When the single unstable fixed point is present and it turns to a stable point due to change in parameter and two new symmetric unstable fixed points occur is called subcritical pitchfork bifurcation.

Answer 7

Chapter 3.6, Problem 3E

Interpretation Introduction

Interpretation:

Sketch the bifurcation diagram by varying parameter a and summarize the result.

Concept Introduction:

By changing the parameter, the fixed points move towards each other, collide, and mutually annihilate is known as the saddle node bifurcation.

The stabilities of the fixed points interchanged by changing the parameter is known as the transcritical bifurcation.

When the single stable fixed point is present and it turns to unstable fixed point due to change in parameter and two new symmetric stable fixed points occur is called supercritical pitchfork bifurcation.

When the single unstable fixed point is present and it turns to a stable point due to change in parameter and two new symmetric unstable fixed points occur is called subcritical 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

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