Abstract
The mechanisms by which the individual functional unit (nephron) of the kidney regulates the incoming blood flow give rise to a number of nonlinear dynamic phenomena, including period-doubling bifurcations and intra-nephron synchronization between two different oscillatory modes. Interaction between the nephrons produces complicated and time-dependent inter-nephron synchronization patterns. In order to understand the processes by which a pair of vascular coupled nephrons synchronize, the paper presents a detailed analysis of the bifurcations that occur at the threshold of synchronization. We show that, besides infinite cascades of saddle-node bifurcations, these transitions involve mutually connected cascades of torus and homoclinic bifurcations. To illustrate the broader range of occurrence of this bifurcation structure for coupled period-doubling systems, we show that a similar structure arises in a system of two coupled, non-identical Rössler oscillators.
| Original language | English |
|---|---|
| Journal | Chaos (Woodbury, N.Y.) |
| Volume | 21 |
| Issue number | 3 |
| Pages (from-to) | 033128 |
| Number of pages | 13 |
| DOIs | |
| Publication status | Published - 19 Jul 2011 |
Keywords
- Animals
- Feedback, Physiological
- Humans
- Kidney Tubules, Proximal
- Models, Biological
- Nephrons
- Oscillometry
- Pressure
- Rats
- Time Factors