Well, subject to certain constraints. You aren't guaranteed that your equilibria behave the same in the linearization of a nonlinear system if your Jacobian ha

Well, subject to certain constraints. You aren't guaranteed that your equilibria behave the same in the linearization of a nonlinear system if your Jacobian has any eigenvalues with real part of 0. https://en.wikipedia.org/wiki/Hartman%E2%80%93Grobman_theorem https://en.wikipedia.org/wiki/Hartman%E2%80%93Grobman_theore...