Self-pulsing dynamics of ultrasound in a magnetoacoustic resonator
  A theoretical model of parametric magnetostrictive generator of ultrasound is considered, taking into account magnetic and magnetoacoustic nonlinearities. The stability and temporal dynamics of the system is analized with standard techniques revealing that, for a given set of parameters, the model presents a homoclinic or saddle--loop bifurcation, which predicts that the ultrasound is emitted in the form of pulses or spikes with arbitrarily low frequency. 
V.J. Sanchez-Morcillo, J. Redondo, J. Martinez-Mora, V. Espinosa and   F. Camarena