Solutions for a three‐dimensional non‐linear stabilized oscillator

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.