Solution: In Exercises 9–14, classify the origin as an

Chapter 5, Problem 10E

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QUESTION:

Problem 10E

In Exercises 9–14, classify the origin as an attractor, repeller, or saddle point of the dynamical system

Find the directions of greatest attraction and/or repulsion.

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QUESTION:

Problem 10E

In Exercises 9–14, classify the origin as an attractor, repeller, or saddle point of the dynamical system

Find the directions of greatest attraction and/or repulsion.

ANSWER:

Solution 10E

Step 1

Consider the following dynamical system:

, where .

To find the solution for the equation , first find the Eigen values of  are the corresponding eigenvectors.

Compute the characteristic polynomial of the matrix :

The roots of the characteristic polynomial are the Eigen values of the matrix .

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