  The basic formulation describing quadratic mode coupling in rotating
Newtonian stars is presented, focusing on polar modes. Due to the
Chandrasekhar-Friedman-Schutz mechanism, the f-mode (fundamental oscillation)
is driven unstable by the emission of gravitational waves. If the star falls
inside the so-called instability window, the mode's amplitude grows
exponentially, until it is halted by nonlinear effects. Quadratic perturbations
form three-mode networks inside the star, which evolve as coupled oscillators,
exchanging energy. Coupling of the unstable f-mode to other (stable) modes can
lead to a parametric resonance and the subsequent saturation of its amplitude,
thus suppressing the instability. The saturation point determines the amplitude
of the gravitational-wave signal obtained from an individual source, as well as
the evolutionary path of the latter inside the instability window.
