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
Topic Video
Question

13-

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

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Knowledge Booster
Discrete Probability Distributions
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,