The instability of dry friction

Based on Newton Dynamics, the kinetic force of friction of any moving object can be found by using formula,

$$F_f = \mu_k F_N$$

This means that if $\mu_k$ and $\ F_N$ remains constant, the force of friction would always be constant.

However, I just read an article and it says that "dry friction can induce several types of instabilities in mechanical systems which display a stable behaviour in the absence of friction.These instabilities may be caused by the decrease of the friction force with an increasing velocity of sliding..." Can we still apply the formula $\ F_f = \mu_k F_N$ when taking this instability into consideration? If so, what changes result in the change of friction- $\mu_k$ or $\ F_N$ ?

The formula you gave for kinetic friction, $$F_f=\mu_kF_N,$$ is a first-order, simplistic, phenomenological model. It describes systems for which the contact surfaces are uniform in space and time.