Find all the fixed points of the system $f(x,y)=-x+x^3, g(x,y)=-2y$ and use linearization to classify them.
I have found the solutions to be : $x = 0$ or $x = ±1$ and $y = 0 \implies 3$ fixed points $(0, 0), (1, 0) $and$ (−1, 0)$
We then calculate the Jacobian matrix, which I did for each of the above fixed points. However, my only concern is that once I calculate the Jacobian matrix at each FP how do I know whether it is a stable, saddle, or unstable node?