| Abstract: | A system of coupled non-linear equations, describing a three-phase stabilized oscillator, is analysed by introducing ‘cyclotomic’ co-ordinates. We show that this system, under certain conditions, approaches asymptotically non-conservative linear systems; and yet it does have stabilized solutions (limit cycles). The non-linear system is solved analytically for an important class of stabilizing functions. We show that the frequency ω of our oscillator responds instantaneously to changes of certain parameters. This result has useful applications in building quickly responding novel electronic voltage-controlled oscillators. |
