Solved: In Exercises 3–6, solve the initial value problem

Chapter 5, Problem 4E

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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.

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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 .

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