On the steady-state phase distribution in a hexagonally coupled oscillator array

The distribution of the phase of the oscillations of a set of mutually injection locked electronic oscillators is investigated for the case of a hexagonal nearest neighbor coupling topology. It is shown that planar distributions are not, in general, steady-state solutions of the system of nonlinear differential equations governing the system. An exact steady-state solution of the equations is obtained and shown to be planar only for six discrete azimuth angles. The degree of deviation from a planar distribution is determined and its impact on the directivity of a phased array excited by the oscillator output signals is estimated.