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Synchronization phenomena in the kidney

Erik Mosekilde

Department of Physics, The Technical University of Denmark, 2800 Lyngby, Denmark

Niels-Henrik Holstein-Rathlou

Department of Medical Physiology, The University of Copenhagen, 2200 Copenhagen N, Denmark

Olga V. Sosnovtseva

Physics Department, Saratov State University, Saratov 410026, Russia

The pressure and flow regulation in the individual functional unit of the kidney (the nephron) tends to operate in an unstable regime. For normal rats, the regulation displays regular self-sustained oscillations, but for rats with high blood pressure the oscillations become chaotic. The lecture explains the mechanisms responsible for this behavior and discusses the involved bifurcations. Experimental data show that neighboring nephrons adjust their pressure and flow regulation in accordance with one another. For rats with normal blood pressure, in-phase as well as anti-phase synchronization can be observed. For spontaneously hypertensive rats, indications of chaotic phase synchronization are found. Accounting for a hermodynamics as well as for a vascular coupling between nephrons that share a common interlobular artery, the lecture presents a model of the interaction of the pressure and flow regulation between adjacent nephrons. It is shown that this model, with physiologically realistic parameter values, can reproduce the different types of experimentally observed synchronization.

References
Holstein-Rathlou N-H, Yip K-P, Sosnovtseva O V and Mosekilde E 2001 Chaos 11 417
Mosekilde E, Maistrenko Yu and Postnov D 2002 Chaotic Synchronization - Applications to Living Systems (World Scientific, Singapore)

Chaotic synchronization of time-continuous oscillators

Erik Mosekilde

Department of Physics, The Technical University of Denmark, 2800 Lyngby, Denmark

Sergiy Yanchuk

Institute of Mathematics, National Academy of Sciences, Kiev, 252601 Ukraine

Considering two coupled identical Rössler oscillators the lecture first discusses the necessary and sufficient conditions for stability of the synchronized chaotic state. The lecture continues to examine the transitions through which low periodic orbits embedded in the synchronized chaotic state lose their transverse stability and produce the characteristic picture of riddled basins of attraction. We also discuss the distinction between local and global riddling and illustrate the further development of the asynchronous periodic orbits.

A similar approach is applied to a model of two interacting biological cells. Considering a prototypic model of the bursting oscillations in insulin producing pancreatic cells, we first present one- and two-dimensional bifurcation diagrams of the individual cell. These diagrams reveal a squid-formed area of chaotic dynamics in parameter space with period-doubling bifurcations on one side and saddle-node bifurcations on the other. The transition from this structure to the so-called period-adding structure is found to involve a subcritical period-doubling and the emergence of type-III intermittency. Finally, the lecture addresses the issue of the robustness of the synchronized chaotic state to a mismatch of the parameters between the interacting oscillators.

References
Yanchuk S, Maistrenko Yu, Lading B and Mosekilde E 2000 Int. J. Bifurcation and Chaos 10 2629
Mosekilde E, Maistrenko Yu and Postnov D 2002 Chaotic Synchronization - Applications to Living Systems (World Scientific, Singapore)


next up previous
Next: Nakamura Up: Abstracts Previous: McClintock