Sideband attraction via internal resonance in a multimode membrane as a mechanism for frequency combs

We study how a driven low-frequency mode couples with an undriven high-frequency mode in a membrane system, creating phononic frequency combs through limit cycles. Using a pump-noisy-probe technique, we show that blue-detuned sidebands attract to the high mode and merge at Hopf bifurcations, revealing the microscopic origin of frequency-comb formation with applications in sensing and phononic metamaterials.