  The so-called chaotic states that emerge on the model of $XY$ interacting on
regular critical range networks are analyzed. Typical time scales are extracted
from the time series analysis of the global magnetization. The large spectrum
confirms the chaotic nature of the observable, anyhow different peaks in the
spectrum allows for typical characteristic time-scales to emerge. We find that
these time scales $\tau(N)$ display a critical slowing down, i.e they diverge
as $N\rightarrow\infty$. The scaling law is analyzed for different energy
densities and the behavior $\tau(N)\sim\sqrt{N}$ is exhibited. This behavior is
furthermore explained analytically using the formalism of
thermodynamic-equations of the motion and analyzing the eigenvalues of the
adjacency matrix.
