Suppose the jacobian matrix of an equilibrium point is time-dependent, as in the second case of Carlos' answer on this question: Jacobian matrix of time dependant system.
Did you know about some reference to deal with stationary points on this case? How to measure stability? I mean, I have a stationary point $X$ and the Jacobian is $t$-dependent. When this does not occur, I calculate the Jacobian on $X$. But now it's not sufficient. Which $t$ should I choose to analyse stability?
Thank you in advance for any comment.
For definition of stability for non-autonomous systems, see page 44 to page 45 of Mathematical Definition of Stability of Non-autonomous Systems.
For criterion for such stability relating to Jacobian, see Hartman–Grobman theorem, A generalization of Hartman's linearization theorem, and On the linearization theorem for nonautonomous differential equations.