This paper presents a nonlinear dynamic model for the purpose of modeling vowels uttered by patients who have problem in the control of voice box muscles. The proposed model will be utilized in the detection of speech pathologies and also automatic speech recognition systems to enhance patients' communication capabilities. The model of this study utilizes feedback, and also a sigmoid nonlinear function which is not included in the linear speech production models. The nonlinear function allows for the higher order dynamics of the signal to be captured and feedback increases dynamicity of the model. The model of the current research was applied to discriminate between few voice pathologies and normal cases. The statistical analysis of the parameters of the trained model showed that these parameters can provide independent and distinct features with which pathological classes can be discriminated.