Determination of linear growth rates of three different seeded overstable modes (indicated by their radial mode number n) in N-body simulations for different values of the nonlinearity parameter q, quantifying the amount of perturbation in the ground state that corresponds to a density wave. Left panels: time evolution of amplitudes A_n (Eq. (66)) with a sampling interval of one orbital period. Right panels: resulting growth rates obtained from linear fits as drawn in the left frames. The simulations used time-averaged values of the ground state optical depth and surface mass density of τ₀ = 1.5 and σ₀ = 300 kg m⁻², respectively, as well as a vertical frequency enhancement of Ω_z∕Ω = 2 to mimic vertical self-gravity.