- #1

- 16

- 0

## Homework Statement

A Lorenz system is given by

x' = sy - sx

y' = 3sx - y - xz

z' = xy - bz

In the vicinity of point x = y = 2s, z=4s , for s>>b, show motion is aligned with the y,z plane (

*sub these values in and x' is 0).*By considering the evolution of vectors [2,0,1+sqrt(5)] , [0,1,0], [1+sqrt(5),0,-2] , or otherwise, estimate the directions in which perturbations grow and contract fastest.

## Homework Equations

I've calculated Jacobian + Jacobian transpose / 2 is:

-s 2s s

2s -1 0

s 0 b

## The Attempt at a Solution

No idea, other than get rid of b then operate with the matrix on the perturbation vectors. The vectors are clearly not eigenvectors though. Setting b = 0 does not return any sensible eigenvectors or values, and trying to solve for the eigenvalues with b small, but non-zero descends into a mess.

Many thanks for any help