Continuing 17, show that the critical point (0, 0) is a. Asymptotically stable if q > 0

Chapter 9, Problem 18

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QUESTION:

Continuing 17, show that the critical point (0, 0) is a. Asymptotically stable if q > 0 and p < 0; b. Stable if q > 0 and p = 0; c. Unstable if q < 0 or p > 0. The results of 17 and 18 are summarized visually in Figure 9.1.8. 1

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QUESTION:

Continuing 17, show that the critical point (0, 0) is a. Asymptotically stable if q > 0 and p < 0; b. Stable if q > 0 and p = 0; c. Unstable if q < 0 or p > 0. The results of 17 and 18 are summarized visually in Figure 9.1.8. 1

ANSWER:

Step 1 of 4

We have the characteristic equation as

         

And the Eigenvalues are given by  

Where  

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