🚀 go-pugleaf

Given a discrete nonlinear dynamical system that depends
on a parameter (say h), is it possible that the linearized stability
around that equilibrium point results in a value of the
parameter that differs from the value that is identified
by simulating the dynamics of the system on a computer ?
(i.e. let's say that the linearized stability requires
h <= h1, and by running a simulation of the system we
result in h <= h2, with h1 < h2, the starting points of for
the simulation are arbitrarily depending on the accuracy of the
machine..., close to the equilibrium point.)
I know that linear stability analysis precludes such a possibility.

Thank you,
ioannis