EBK NONLINEAR DYNAMICS AND CHAOS WITH S
EBK NONLINEAR DYNAMICS AND CHAOS WITH S
2nd Edition
ISBN: 9780429680151
Author: STROGATZ
Publisher: VST
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Chapter 5.2, Problem 4E
Interpretation Introduction

Interpretation:

Find characteristic polynomial for the system of linear equations, x˙ =  5x+10y and y˙ = -x -y using x˙ = Ax equation. Also find eigenvalues and eigenvectors.

Solve the given system of linear equations and write the general solution.

Classify the fixed points at the origin.

Concept Introduction:

Equations for two dimensional linear system are x˙ = ax + by, y˙ = cx + dy.

Above linear system expressed in the form x˙ = Ax.

The standard characteristic polynomial is

λ2- τλ + Δ = 0, where τ is trace of matrix A, λ is corresponding eigenvalue, and Δ is determinant of matrix A.

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