Analysis of a symmetrically stabilized three-dimensional oscillator and some implications

A recently suggested symmetrically constructed three-dimensional oscillator model is analysed. It is proved by using Lyapunov’s stability theory that the system possesses two main steady states. In one of the steady states the solutions are three sinusoids arranged symmetrically (like the voltages of a three-phase electric AC supply system). The second steady state is such that all three solutions approach the same constant value when time increases. The system can be viewed as consisting of two parts: a conservative oscillator model, and non-linear terms which introduce damping forces responsible for stabilizing the waveforms in steady state. The dynamic behaviour of the system can be interpreted in view of its structural properties and symmetrically cyclic topology. The features of the system structure and the properties of its dynamic behaviour suggest that it can be employed as a simplified model for representing synchronous generators in largo power systems simulations. Another application of the system is as a model for constructing a precise electronic function generator.