Abstract
In the body there are several natural oscillations, such as blood flow and blood sugar levels in diabetes. There is also oscillatory behaviour in the flow of the functional unit within the kidney called the nephron. Our aim is to consider a model of the nephron in order to better understand how these oscillations come about and what factors effect them. We present a model that has been shown to demonstrate the behaviour of the experimentally observed results. This model incorporates a delay to represent the fluid transit in part of the nephron. We then look at various form of the delay. By changing the delay form we end up with both an ordinary differential equation model and a delay differential equation model. We discuss how to analyse the model analytically but find that, since this results in highly non-linear coupled equations analytical progress is difficult. A variety of numerical analysis techniques are used on the systems in order to produce insights into the bifurcation structure. These results show qualitatively similar results for the different forms of the delay that we consider, but there are quantitative differences which suggest that quantitative comparison with experimental data would be difficult without a thorough understanding of the form of the delay.