Find the equilibria of x4-1= 4x +x4 - 36, t= 0, 1, 2,... and use the stability criterion for an equilibrium point to determine whether they are stable or unstable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The stable equilibria are N= and the unstable equilibria are N=| (Type integers or simplified fractions. Use a comma to separate answers as needed.) O B. The unstable equilibria are N= There are no stable equilibria. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O C. The stable equilibria are N= There are no unstable equilibria. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) O D. There are no equilibria.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Find the equilibria of \( x_{t+1} = 4x_t^2 + x_t - 36 \), \( t = 0, 1, 2, \ldots \), and use the stability criterion for an equilibrium point to determine whether they are stable or unstable.

Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

- A. The stable equilibria are \( N = \) [ ] and the unstable equilibria are \( N = \) [ ].
  (Type integers or simplified fractions. Use a comma to separate answers as needed.)

- B. The unstable equilibria are \( N = \) [ ]. There are no stable equilibria.
  (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

- C. The stable equilibria are \( N = \) [ ]. There are no unstable equilibria.
  (Type an integer or a simplified fraction. Use a comma to separate answers as needed.)

- D. There are no equilibria.
Transcribed Image Text:Find the equilibria of \( x_{t+1} = 4x_t^2 + x_t - 36 \), \( t = 0, 1, 2, \ldots \), and use the stability criterion for an equilibrium point to determine whether they are stable or unstable. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. - A. The stable equilibria are \( N = \) [ ] and the unstable equilibria are \( N = \) [ ]. (Type integers or simplified fractions. Use a comma to separate answers as needed.) - B. The unstable equilibria are \( N = \) [ ]. There are no stable equilibria. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) - C. The stable equilibria are \( N = \) [ ]. There are no unstable equilibria. (Type an integer or a simplified fraction. Use a comma to separate answers as needed.) - D. There are no equilibria.
Expert Solution
Step 1

Consider the given equation whose stability id to check.

Advanced Math homework question answer, step 1, image 1

Step 2

For part (a) it is required to use the stability criterion to characterize the stability of the equilibria.

Advanced Math homework question answer, step 2, image 1

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