In this paper, dynamics in the oscillations of the relative atomic population in two periodically driven and weakly coupled Bose-Einstein condensates (BECs) was qualitatively studied. Using the well-known Melnikov method, the conditions of existence of the periodic and chaotic coherent atomic tunnellings were given in the model. Our results indicate the typical route from bifurcation of the limited circles to chaos, and are in agreement with the previous numerical results.