I am not sure if there's a single answer to my questions:
- How can I find out if it's possible to escape from a point of a vector field by following the flow? There's a sub condition: It's not sufficient that the field is 0 at that point, but all surrounding vectors have to be 0 as well or to point inwards - like a stable equilibrium.
- How can the same be done for a point that lies inside a region or on a region that possibly can't be left?
Is there a simple way to calculate the region of confinement?
Perhaps of relevance: All values are real and the problem is 3n-dimensional.
Thanks in advance!
Edit: A simple example would be f(x,y)=(-1-x+x²,1-y). I think it could be possible to find such points with the conditions f(x,y)=(0,0) & $(\partial_x f(x,y))_x<0$ & $(\partial_y f(x,y))_y<0$. In this example the sought point is $(\frac{1}{2} \left(\sqrt{5}+1\right),1)$. But that does not look nice. Plot of the example: example flow
