Hey MHF,
So I am working through the Lorenz Equations and have run into a road block that has stumped me all day, I have turned to my beloved internet for help again.
So I have managed to work through the system of equ.
and have used θ=10 and b=8/3... I know original... which gives me this matrix:::
Now I get stumped on producing the right the eigenvectors, which is a laborious process most of the time but it was beyond me today...
anyways, Eigenvalues are
λ= -8/3
λ= (-11-(81+40r)^(1/2))/2 and
λ= (-11+(81+40r)^(1/2))/2
Duhhh... this is easy but when I use λ= -8/3
I do not get the ε=(0,0,1) which my solutions say I should get....
Instead I get something like:
22/3ε1=10ε2
I am so very lost....Could someone please point me in the right direction.
FernandoRevilla! Thank you! The determinate of the matrix was the icing on the cake.
Thanks for the concern Ackbeet, I forgot to include the fact that I input Lorenz's equations into a Jacobian Matrix. Which looks at locally linear systems around point (x,y,z). My bad. I'm always skipping steps...