I'm muddling my way through Strogatz Nonlinear Dynamics and Chaos, and I've run into something I'm too dumb to understand.
In example $6.6.3$, he gives us a system:
$\dot x = 2 \cos x - \cos y$
$\dot y = 2 \cos y - \cos x$
And gives us a Jacobian of (where x* and y* are the critial points and x*=y*)
$\begin{bmatrix} 2\sin x* && \sin x* \\ \sin x* && 2\sin x* \end{bmatrix}$
But when I take the partial derivatives like he shows in section 6.3, I get
$\begin{bmatrix} -2\sin x* && \sin y* \\ \sin x* && -2\sin y* \end{bmatrix}$
I get that he showed x*=y*, but where did the negative signs go?
Apologies again for not being able to figure out the formatting, I'm stuck on mobile due to a dead computer.
I checked the book and it says that the dynamical system is
$\dot x = -2 \cos x - \cos y$
$\dot y = -2 \cos y - \cos x$
Which is not the same that you wrote. What you did it's fine for that dynamical system.