The dynamical system x ′ = − α x + x y and y ′ = 1 − β y − x 2 has a unique critical point if α β > 1 and the it is stable if β > 0 .

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Answer 1

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Chapter 11.3, Problem 28E

To determine

To show: The dynamical system x′=−αx+xy and y′=1−βy−x2 has a unique critical point if αβ>1 and the it is stable if β>0.

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Answer 2

Question

Chapter 11.3, Problem 28E

To determine

To show: The dynamical system x′=−αx+xy and y′=1−βy−x2 has a unique critical point if αβ>1 and the it is stable if β>0.

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Answer 3

Question

Chapter 11.3, Problem 28E

To determine

To show: The dynamical system x′=−αx+xy and y′=1−βy−x2 has a unique critical point if αβ>1 and the it is stable if β>0.

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Answer 4

Question

Chapter 11.3, Problem 28E

To determine

To show: The dynamical system x′=−αx+xy and y′=1−βy−x2 has a unique critical point if αβ>1 and the it is stable if β>0.

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Answer 5

Chapter 11.3, Problem 28E

To determine

To show: The dynamical system x′=−αx+xy and y′=1−βy−x2 has a unique critical point if αβ>1 and the it is stable if β>0.

Answer 6

Chapter 11.3, Problem 28E

To determine

To show: The dynamical system x′=−αx+xy and y′=1−βy−x2 has a unique critical point if αβ>1 and the it is stable if β>0.

Answer 7

Chapter 11.3, Problem 28E

To determine

To show: The dynamical system x′=−αx+xy and y′=1−βy−x2 has a unique critical point if αβ>1 and the it is stable if β>0.

Answer 8

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Answer 9

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Answer 10

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Answer 11

Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E Ch. 11.1 - Prob. 6E Ch. 11.1 - Prob. 7E Ch. 11.1 - Prob. 8E Ch. 11.1 - Prob. 9E Ch. 11.1 - Prob. 10E

The dynamical system x ′ = − α x + x y and y ′ = 1 − β y − x 2 has a unique critical point if α β > 1 and the it is stable if β > 0 .

Solution Summary: The author analyzes the dynamical system xprime, which has a unique critical point if alpha >1 and the it is stable.

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To show: The dynamical system x′=−αx+xy and y′=1−βy−x2 has a unique critical point if αβ>1 and the it is stable if β>0.

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Chapter 11 Solutions

The dynamical system x ′ = − α x + x y and y ′ = 1 − β y − x 2 has a unique critical point if α β &gt; 1 and the it is stable if β &gt; 0 .

Solution Summary: The author analyzes the dynamical system xprime, which has a unique critical point if alpha >1 and the it is stable.

Concept explainers

Videos

To show: The dynamical system x′=−αx+xy and y′=1−βy−x2 has a unique critical point if αβ>1 and the it is stable if β>0.

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Chapter 11 Solutions

The dynamical system x ′ = − α x + x y and y ′ = 1 − β y − x 2 has a unique critical point if α β > 1 and the it is stable if β > 0 .