C-type period-doubling transition in nephron autoregulation

The functional units of the kidney, called nephrons, utilize mechanisms that allow the individual nephron to regulate the incoming blood flow in response to fluctuations in the arterial pressure. This regulation tends to be unstable and to generate self-sustained oscillations, period-doubling bifurcations, mode-locking and other nonlinear dynamic phenomena in the tubular pressures and flows. Using a simplified nephron model, the paper examines how the regulatory mechanisms react to an external periodic variation in arterial pressure near a region of resonance with one of the internally generated mode-locked cycles. We show how the stable and unstable resonance cycles generated in this response undergo interconnected cascades of period-doubling bifurcations and how each period doubling leads to the formation of a new pair of saddle-node bifurcation curves along the edges of the resonance zone. We also show how period doubling of the resonance cycles is accompanied by a torus-doubling process in the quasiperiodic regime that exists outside of the resonance zone.