I have Non Linear Dynamic Systems for which I have computed the fixed points, and now I wish to investigate the nature of these points (primarily whenever they are stable or not). I understand that the way to do so is to compute the Jacobian of the system and then to find its Eigenvalues in the fixed point. If all have real part less than 0 the point is stable, otherwise not.
Now, will looking all this up I found a so called "Poincaré Diagram" on wikipedia (https://en.wikipedia.org/wiki/Stability_theory). No actual information was given on it and I have not found anything else on it. However, it seemed very useful. Exactly for what systems does this one hold? Can I actually use it for systems with more than 2 variables?
Finally, if I cannot use this so called Poincaré Diagram, is there a good way to determine whenever you have oscillations around a fixed point?
Cheers