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23. Consider the system *-()*. a. Solve the system for a = . What are the eigenvalues of the coefficient matrix? Classify the equilibrium point at the origin as to type. b. Solve the system for a = 2. What are the eigenvalues of the coefficient matrix? Classify the equilibrium point at the origin as to type. c. In parts a and b. solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of a, and determine the value of a between and 2 where the transition from one type of behavior to the other occurs. This value of a is called a bifurcation value for this problem.

23. Consider the system *-()*. a. Solve the system for a = . What are the eigenvalues of the coefficient matrix? Classify the equilibrium point at the origin as to type. b. Solve the system for a = 2. What are the eigenvalues of the coefficient matrix? Classify the equilibrium point at the origin as to type. c. In parts a and b. solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of a, and determine the value of a between and 2 where the transition from one type of behavior to the other occurs. This value of a is called a bifurcation value for this problem.

Advanced Engineering Mathematics
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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23. Consider the system a. Solve the system for a = 1. What are the eigenvalues of the coefficient matrix? Classify the equilibrium point at the origin as to type. x - (- - -1) x. x' = b. Solve the system for a = 2. What are the eigenvalues of the coefficient matrix? Classify the equilibrium point at the origin as to type. e. In parts a and b, solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of a, and determine the value of a between 1 and 2 where the transition from one type of behavior to the other occurs. This value of a is called a bifurcation value for this problem.
Transcribed Image Text:23. Consider the system a. Solve the system for a = 1. What are the eigenvalues of the coefficient matrix? Classify the equilibrium point at the origin as to type. x - (- - -1) x. x' = b. Solve the system for a = 2. What are the eigenvalues of the coefficient matrix? Classify the equilibrium point at the origin as to type. e. In parts a and b, solutions of the system exhibit two quite different types of behavior. Find the eigenvalues of the coefficient matrix in terms of a, and determine the value of a between 1 and 2 where the transition from one type of behavior to the other occurs. This value of a is called a bifurcation value for this problem.
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