Activator-repressor systems have been shown to
be capable of oscillations and are therefore an important clock
motif in the field of Synthetic and Systems Biology. In this paper,
we propose a method to regulate oscillatory behavior in such
systems by the addition of DNA binding sites for the proteins
involved in the clock network. We show that the retroactivity
effect caused by this addition can effectively change the relative
timescales among the protein dynamics and impact the behavior
of the clock. We also employ root locus analysis to obtain a
graphical interpretation of the results
