We propose a theoretical description and experimental validation of a frequency self-stabilized photonic oscillator. This photonic oscillator which relies on a solid-state laser and a nonreciprocal Brillouin fiber resonator (BFR) arranged in an optical phase-locked loop (OPLL) was recently shown to provide very narrow linewidth in the Hz range. Special attention is given to end up with analytical expressions relying on coupled-mode formalism, of the BFR dynamics in which the non-resonant configuration for the pump has to be addressed. Furthermore, the transfer function of the full system is derived from the response of each component within the OPLL leading to two interleaved loops, relative to the phase and to the amplitude fluctuations of the optical field. An experimental setup including a solid-state Er:Yb laser is detailed and used to test the model predictions, both for phase noise level and response time. This model opens the way to the optimization of this new type of photonic oscillator which can be adapted to any kind of pump laser.