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This paper describes a study of the effects of variations in the thalamocortical synaptic activity on alpha rhythms (8 - 13 Hz) using a computational model. The study aims to investigate alpha rhythm slowing associated with Alzheimer's Disease. It is observed that for a certain range of values of the input, an increase in inhibitory activity results in an increase of the lower alpha band (8 - 10 Hz) power and a corresponding decrease in the upper alpha band (11 - 13 Hz) power, thus indicating a slowing of the alpha rhythms. On the other hand, an increase in the excitatory synaptic activity results in an overall shift of the peak power in the output signal from the lower alpha band to the upper alpha band. However, for values of input outside this range, the output signal shows a bifurcation in behaviour and enters a limit cycle mode. In this state, the output power lies dominantly in the lower alpha band. Variation in the inhibitory or excitatory synaptic parameters has little or no effect on the frequency band of the output power.