We derive the modified rate equations for an Aharonov-Bohm (AB) ring with two transversely coupled quantum dots (QD's) embedded in two arms in the presence of a magnetic field. We find that the interdot coupling between the two QD's can cause a temporal oscillation in electron occupation at the initial stage of the quantum dynamics, while the source-drain current decays monotonically to a stationary value. On the other hand, the interdot coupling equivalently divides the AB ring into two coupled subrings. That also destroys the normal AB oscillations with a period of 2pi, and generates new and complex periodic oscillations with their periods varying in a linear manner as the ratio between two magnetic fluxes (each penetrates one AB subring) increases. Furthermore, the interference between two subrings is also evident from the observation of the perturbed fundamental AB oscillation.