The focus of this paper is to correlate the bifurcation behaviour of a thalamocortical neural mass model with the power spectral alpha (8–13 Hz) oscillatory activity in Electroencephalography (EEG). The aim is to understand the neural correlates of alpha rhythm slowing (decrease in mean frequency of oscillation), a hallmark in the EEG of Alzheimer's Disease (AD) patients. The neural mass model used, referred to herein as the modARm, is a modified version of Lopes da Silva's alpha rhythm model (ARm). Previously, the power spectral behaviour of the modARm was analysed in context to AD. In this work, we revisit the modARm to make a combined study of the dynamical behaviour of the model and its power spectral behaviour within the alpha band while simulating the hallmark neuropathological condition of ‘synaptic depletion’ in AD. The results show that the modARm exhibits two ‘operating modes’ in the time-domain i.e. a point attractor and a limit cycle mode; the alpha rhythmic content in the model output is maximal at the vicinity of the point of bifurcation. Furthermore, the inhibitory synaptic connectivity from the cells of the Thalamic Reticular Nucleus to the Thalamo-Cortical Relay cells significantly influence bifurcation behaviour—while a decrease in the inhibition can induce limit-cycle behaviour corresponding to abnormal brain states such as seizures, an increase in inhibition in awake state corresponding to a point attractor mode may result in the slowing of the alpha rhythms as observed in AD. These observations help emphasise the importance of bifurcation analysis of model behaviour in inferring the biological relevance of results obtained from power-spectral analysis of the neural models in the context of understanding neurodegeneration.