kidsmoker
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Homework Statement
http://img195.imageshack.us/img195/4873/46343978.jpg
The Attempt at a Solution
Part (a) is simple enough, i get
\dot{x}=y
\dot{y}=x^{3}-x.
Equilibrium points occur when the time-derivatives of both x and y are zero, which gives the 3 equilibrium points (0,0), (1,0) and (-1,0).
Now I thought i'd better write it as a matrix equation as this is how i remember doing these type of problems, so if we write
X=\begin{pmatrix}x \\ y \end{pmatrix} then
\dot{X}=\begin{pmatrix} 0 & 1 \\ x^{2}-1 & 0 \end{pmatrix}X
(sorry, you have to look closely to see where the dots are!).
I would have thought i'd then have to find the eigenvales of this matrix for each of my equilibrium points to find the stability of each one? But when I look at the solution, it uses the Jacobian matrix and finds the eigenvalues of that instead?! I'm confused!
Thanks for any help!
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