Ultrasubharmonic resonance and nonlinear dynamics in the song of Oecanthus nigricornis F. Walker (Orthoptera : Gryllidae)

In the few cricket species that have been studied, there is a 1 : 1 relationship between carrier frequency and tooth-strike rate in normal song. However, for the vast majority of cricket species that relationship remains unknown. In the tree cricket, Oecanthus nigricornis F. Walker (Orthoptera : Gryllidae : Oecanthinae), the carrier frequency of the song normally equals the tooth-strike rate; rarely, the two are different and phase-locked in ultrasubharmonic ratios, such as 4 : 3 or 5 : 4. Sometimes, both frequencies are simultaneously present, giving rise to acoustic beats with 2 sharp frequency peaks related by similar ratios. The above phenomena were artificially induced in normal live singing crickets by experimental modification of one or both tegmina: beats arise when one of the tegmina vibrates at the tooth-strike frequency, while the other vibrates at the ultrasubharmonic frequency. A mathematical model is presented of the Oecanthus tegminal resonator, consisting of 2 simple coupled differential equations, one of them with a nonlinear restoring term. Integration of the model at various values of tooth-strike rate and exciting force, yields all of the observed phenomena, including normal and ultrasubharmonic output frequencies as well as beats between them. The resulting waveforms and acoustic spectra accurately reproduce those found in natural and experimental recordings.