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 6E
Interpretation Introduction

Interpretation:

Find the characteristic polynomial for the system of linear equations x˙ = -3x + 2y and y˙ = x - 2y using x˙ = Ax equation. Also, find the eigenvalues and the eigenvectors of matrix A.

To find the general solution for the given system of linear equations.

Classify the fixed points at the origin.

Concept Introduction:

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

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

The standard characteristics polynomials is,

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

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10 5 Obtain by multiplying matrices the composite coordinate transformation of two transformations, first x' = (x + y√√2+2)/2 y' = z' (x√√2-2√2)/2 z = (-x+y√√2-2)/2 followed by x" = (x'√√2+z'√√2)/2 y" = (-x'y'√√2+2')/2 z" = (x'y'√√2-2')/2.
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