This paper reports a study on short-time subharmonic pitch breaks in vocal fold vibration, which are found to be a common feature of the human voice in spoken language. The observed pitch breaks correspond to a change in periodicity of the electrolaryngograph (Lx) signal. This paper presents a nonlinear dynamical system capable of producing time-series with subharmonic pitch breaks. The resulting time-series resemble closely Lx recordings of natural speech. The system is developed on the basis of a second order linear system, which is extended with a third dimension and nonlinear coupling terms. It is suggested that improved knowledge about pitch breaks could be used in future speech synthesis systems in order to improve the naturalness of the perceived output.