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Solved: In Exercises 3–6, solve the initial value problem
Chapter 5, Problem 4E(choose chapter or problem)
Problem 4E
In Exercises 3–6, solve the initial value problem for . Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by .Find the directions of greatest attraction and/or repulsion. When the origin is a saddle point, sketch typical trajectories.
Questions & Answers
QUESTION:
Problem 4E
In Exercises 3–6, solve the initial value problem for . Classify the nature of the origin as an attractor, repeller, or saddle point of the dynamical system described by .Find the directions of greatest attraction and/or repulsion. When the origin is a saddle point, sketch typical trajectories.
ANSWER:
Solution 4E
Step 1
Consider the following dynamic system with initial condition:
and
Here,
The characteristic polynomial of the matrix :
The Eigen values of the matrix are .