The paper presents extensions of the single-matrix formulation (Mokhtari et al., 2008, Speech Comm. 50(3) 179 – 190) that enable self-oscillation models of vocal folds, including glottal chinks, to be connected to the vocal tract. It also integrates the case of a local division of the main air path into two lateral channels, as it may occur during the production of lateral approximants. Extensions are detailed by a reformulation of the acoustic conditions at the glottis, and at the upstream connection of bilateral channels. Numerical simulations are provided to validate the simulation framework. The introduction of a zero due to the presence of bilateral channels is confirmed by the simulations. The position of the zero agrees with the theoretical predictions. Simulations of static vowels reveal that the behavior of the vocal folds is qualitatively similar whether they are connected to the single-matrix formulation or to the classic reflection type line analog model. Finally, the acoustic effect of the glottal chink on the production of vowels is highlighted by the simulations: the shortening of the vibrating part of the vocal folds lowers the amplitude of the glottal flow, and therefore lowers the global acoustic level radiated at the lips. It also introduces an offset in the glottal flow waveform.