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Determine the nature of the origin (attractor, repeller,
Chapter 5, Problem 8E(choose chapter or problem)
Determine the nature of the origin (attractor, repeller, or saddle point) for the dynamical system if A has the properties described in Exercise 2. Find the directions of greatest attraction or repulsion.Reference:Suppose the eigenvalues of a 3 × 3 matrix A are 3, 4/5, and
Questions & Answers
QUESTION:
Determine the nature of the origin (attractor, repeller, or saddle point) for the dynamical system if A has the properties described in Exercise 2. Find the directions of greatest attraction or repulsion.Reference:Suppose the eigenvalues of a 3 × 3 matrix A are 3, 4/5, and
ANSWER:Solution 8EStep 1 Consider the dynamical system: ,where is a matrix with Eigenvalues and the Eigenvectors are, .Here, one of the Eigenvalue 3 is greater than 1 in magnitude and an Eigenvalues are less than 1 in magnitude, therefore origin is a saddle point for the dynamical system.