Limit cycles in nonlinear excitation of clusters of classical oscillators

In this paper we develop a numerical procedure for detecting the existence of limit cycles in nonlinear excitation of clusters of classical harmonic oscillators. Our technique is able to compute also the main parameters of a limit cycle, that is the amplitudes and the period. The numerical method, based on the propagation matrix formalism, is transparent and easy to apply. It may find application in various areas where nonlinear excitations are involved, e.g., sound and mechanic vibrations in musical instruments, ground vibrations in volcanic areas, and sea tides.