Nonlinear Dynamics and Chaos
Nonlinear Dynamics and Chaos
2nd Edition
ISBN: 9780813349107
Author: Steven H. Strogatz
Publisher: PERSEUS D
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Chapter 5.2, Problem 9E
Interpretation Introduction

Interpretation:

Find characteristic polynomial for system of linear equations, x˙ = 4x - 3y and y˙ = 8x - 6y  using x˙ = Ax equation. Also find eigenvalues and eigenvectors of matrix A.

For the given system of linear equations, the general solution is found.

Classify the fixed points at the origin.

Concept Introduction:

For two dimensional linear system, the equations are x˙ = ax + by, y˙ = cx + dy.

The above linear system is expressed in the form x˙ = Ax.

The standard characteristics polynomials is

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

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