The article is devoted to the study of the morphology of the phase space of a degenerate two-component mathematical model of a nerve impulse propagation in the membrane shell. A mathematical model is studied in the case when the parameter at the time derivative of the component responsible for the dynamics of the membrane potential is equal to zero, and the theorem about the fact that the phase space is simple in this case is proved. A mathematical model is also considered in the case when the parameter at the time derivative of the component responsible for the ion currents is equal to zero, and the theorem on the presence of singularities of Whitney assemblies is proved. Based on the results obtained, the phase space of the mathematical model is constructed in the case when the parameters at the time derivative of both components of the system are equal to zero. The author gives examples of the construction of the phase space, illustrating the presence of features in the phase space of the studied problems based on the Galerkin method.