I can't give you a thorough answer, but here is some food for thought:
If an electrical dipole is operating "all by itself", it will have done a certain amount of work "on space" to set up an electric field. Now if there is a second dipole nearby, it will also do some work to change the electric field; if these fields add up, the total energy stored will be more than the sum of the individual energies, because energy goes as electric field squared.
This means that when the two dipoles are in phase, the work they have to do for a certain displacement of charge is greater - in other words, there is an apparent restoring force which is greater. This means that the resonant frequency will be increased.
On the other hand, if they are out of phase with each other, they make the stored field smaller, and this results in a reduction of their frequency. So two modes of oscillation will appear: in phase (higher), and out of phase (lower).