On the development of symmetrically stabilized five‐phase oscillators and some implications

The paper deals with the development of a symmetrically stabilized five‐phase oscillator. the development results from two origins. It employs on one hand a five‐phase conservative oscillator. On the other hand the stabilization process of the oscillator is due to similar non‐linear damping terms in earlier developments of stabilized three‐phase oscillators. A new feature of the present system is that it possesses an interesting steady state limit‐cycle behaviour. the two possible steady state oscillations are similar, since both of them consist of a five‐phase balanced set of phasors which are arranged symmetrically. However, each mode of possible steady state oscillation possesses its own unique frequency, although the amplitudes are equal. Another interesting feature of the oscillator is related to the way in which the various possible solutions (oscillatory, steady state, stable and unstable dynamic behaviours) evolve from initial conditions. There seem to exist regions where the system solutions appear sensitive to minute changes in initial conditions. It appears that completely different types of dynamic behaviours can develop from initial conditions in close proximity, which may lead eventually to the development of slightly modified systems with chaotic dynamics. the paper concludes by suggesting an application of multiphase oscillators for feeding phased array antennas.