  Recent results have shown the appearance of induced cooperative motions
called dynamic heterogeneity during the isomerization of diluted azobenzene
molecules in a host glass-former. In this paper we raise the issue of the
coupling between these "artificial" heterogeneities and the isomerization
period. How do these induced heterogeneities differ in the saturation regime
and in the linear response regime ? Is there a maximum of the heterogeneous
motion versus isomerization rate and why ? Are the heterogeneity evolution with
the isomerization rate connected with the diffusion or relaxation time
evolution ? We use out of equilibrium molecular dynamics simulations to answer
these questions. We find that the heterogeneity increases in the linear
response regime for large isomerization periods and small perturbations. In
contrast the heterogeneity decreases in the saturation regime, i.e. when the
isomerization half-period ($\tau_{p}/2$) is smaller than the relaxation time of
the material ($\tau_{\alpha}$). This result makes possible a test of the effect
of cooperative motions on the dynamics using the chromophores as Maxwell demons
that destroy or stimulate the cooperative motions. Because the heterogeneities
increase in the linear regime and then decrease in the saturation regime, we
find a maximum for $\tau_{p}/2 \approx \tau_{\alpha}$. The induced excitations
concentration follows a power law evolution versus the isomerization rate and
then saturates. As a consequence the $\alpha$ relaxation time is related to the
excitation concentration with a power law, a result in qualitative agreement
with recent findings in constrained models. This result supports a common
origin for the heterogeneities with constrained models and a similar relation
to the excitation concentration.
