The reactivity of a coupled core is controlled by a set of control rods distributed in the central reflector region. The reactor contains two compact cores cooled and moderated by light water. Control rods are designed to have reactivity worths sufficient to start, control and shutdown the coupled system. Each core in a coupled system is in subcritical conditions without any absorber then each core needs to the other core to fulfill nuclear chain reaction and to approach the criticality. In this case, each core is considered clean which is suitable for research reactor with low flux disturbance and better neutron economy, in addition to the advantage of disappearing the cut corner fuel baskets. This facilitate the in core fuel management with identical fuel baskets. Hot spots will disappear. This leads to a good heat transfer process. the excess reactivity and the shutdown margin are calculated for some of reflector as coupling region gives sufficient area for coupled core are calculated cost. The fluctuations of reactivity for coupled core are calculated by noise analysis technique and compared with that for rode core. The results show low reactivity perturbation associated with coupled core.