The critical point ( 0 , 0 ) is a stable node for the linear system X ′ = A X when b c < 1 , where A = ( − a x ^ − a b x ^ − c d y ^ − d y ^ ) .

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Answer 1

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Chapter 11.2, Problem 22E

To determine

To show: The critical point (0,0) is a stable node for the linear system X′=AX when bc<1, where A=(−ax^−abx^−cdy^−dy^).

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Determine the type of the critical point (I1,I2) = of the nonlinear system X = f(x), where x= f(x) = -312+21,22] Source Node. Source Spiral. None of the options displayed Saddle Node. Sink Spiral. Center. There is no way to determine the type of the critical point with the information provided. Sink Node

b) Let aggregate national income be given by Y; = Ct + It + Gt Where C, I and G are consumption, investment and government expenditure. Assume that consumption is given by Ct = mY; Investment is given by Iį = i + a(Yt-1 – Yt-2) And government expenditure declines over time according to G; = Go(1 – 8)*, 0 < 8 < 1 Where d is the exogenous rate of decline of government expenditure (i) Derive the linear second order difference equation. (ii) Solve the difference equation.

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Answer 2

Question

Chapter 11.2, Problem 22E

To determine

To show: The critical point (0,0) is a stable node for the linear system X′=AX when bc<1, where A=(−ax^−abx^−cdy^−dy^).

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Answer 3

Question

Chapter 11.2, Problem 22E

To determine

To show: The critical point (0,0) is a stable node for the linear system X′=AX when bc<1, where A=(−ax^−abx^−cdy^−dy^).

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Answer 4

Question

Chapter 11.2, Problem 22E

To determine

To show: The critical point (0,0) is a stable node for the linear system X′=AX when bc<1, where A=(−ax^−abx^−cdy^−dy^).

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Answer 5

Chapter 11.2, Problem 22E

To determine

To show: The critical point (0,0) is a stable node for the linear system X′=AX when bc<1, where A=(−ax^−abx^−cdy^−dy^).

Answer 6

Chapter 11.2, Problem 22E

To determine

To show: The critical point (0,0) is a stable node for the linear system X′=AX when bc<1, where A=(−ax^−abx^−cdy^−dy^).

Answer 7

Chapter 11.2, Problem 22E

To determine

To show: The critical point (0,0) is a stable node for the linear system X′=AX when bc<1, where A=(−ax^−abx^−cdy^−dy^).

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

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 critical point ( 0 , 0 ) is a stable node for the linear system X ′ = A X when b c < 1 , where A = ( − a x ^ − a b x ^ − c d y ^ − d y ^ ) .

Solution Summary: The author explains that the critical point (0,0) is a stable node for the linear system.

To show: The critical point (0,0) is a stable node for the linear system X′=AX when bc<1, where A=(−ax^−abx^−cdy^−dy^).

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Chapter 11 Solutions

The critical point ( 0 , 0 ) is a stable node for the linear system X ′ = A X when b c &lt; 1 , where A = ( − a x ^ − a b x ^ − c d y ^ − d y ^ ) .

Solution Summary: The author explains that the critical point (0,0) is a stable node for the linear system.

To show: The critical point (0,0) is a stable node for the linear system X′=AX when bc<1, where A=(−ax^−abx^−cdy^−dy^).

Want to see the full answer?

Chapter 11 Solutions

The critical point ( 0 , 0 ) is a stable node for the linear system X ′ = A X when b c < 1 , where A = ( − a x ^ − a b x ^ − c d y ^ − d y ^ ) .