Example of a “3D saddle”, however this is not the “official name”, in 3D we don’t distinguish between “nodes”, “spirals”, “saddles”, …:
In general this is referenced as: “2 stable, 1 unstable eigenvectors/eigenvalues”
Example of 2 stable imaginary conjugate, 1 stable eigenvectors:
If instead we have 2 stable imaginary conjugate, 1 unstable eigenvectors:
- Notice how in the phase plane the two conjugate eigenvalues converge to , but the third one diverges.
2 marginally-stable imaginary conjugate, 1 unstable eigenvectors:
- In the phase plane we have 2 sinusodial “constant” function (their amplitdue reamains constant) and 1 exponentially decreasing function.
If instead we have 2 marginally-stable imaginary conjugate, 1 marginally-stable eigenvectors:
- This is an infinite series of separated circles.
- In 3D we don’t distinguish between “stars”, “nodes”, …