Circadian rhythms refer to the physiological and biological processes that fluctuate over a 24-hour period. These rhythms are found in most living things such as animals, plants and fungi. In mammals, circadian rhythms are mainly generated and regulated by the suprachiasmatic nucleus (SCN).The period (Per1) gene in the SCN plays a key role in directing circadian rhythms. Per1 expression increases during the day and decreases at night. The neurons which express the Per1 gene show different behaviours to non-Per1 neurons during the day-night cycle. Per1 neurons are in a state of repetitive firing in the morning while in the late morning they display a bursting behaviour. In the afternoon, Per1 neurons divide into two groups: GA and GB, where GA is in a repetitive firing state and GB is silent. At night, these neurons are generally in a quiescent state but late at night they generate spikes.In this study, a standard Hodgkin-Huxley type model was used to study the behaviours of Per1 neurons over the day-night cycle using bifurcation analysis. In this model, the potassium and calcium currents carry the circadian rhythms which are modelled by their conductance. The currents had a significant impact on Per1 neuron behaviours. Furthermore, by changing some of the model parameters, different bistability mechanisms were examined.The study was extended to explore the effect of noise from other neurons on Per1 neuron behaviours. It was shown that noise plays a crucial role in inducing some of the Per1 neuron behaviours and that some Per1 neuron behaviours are fully induced by this noise, e.g. the late morning and late night behaviours. In contrast, the noise was found not to have any significant effect on other Per1 neuron behaviours other than the two behaviours that are observed in the afternoon.