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DY: Fachverband Dynamik und Statistische Physik

DY 2: Statistical Physics in Biological Systems I (joint with BP)

DY 2.2: Vortrag

Montag, 11. März 2013, 09:45–10:00, H47

Extended diffusion models for sleep stage switching — Anna Barkentien and •Jens Christian Claussen — INB, University of Lübeck, Germany

Short awakening periods especially occuring during the second half of the night follow a peculiar power law [1] for which biologically plausible models still are not available. A pure Markov analysis [2] assuming random switching however ignores any deterministic components in the dynamics which are manifest in time correlations. The phenomenological model proposed in [1] describes sleep depth by a one-dimensional diffusion process with a reflecting border for sleep and a restoring force for wake. In contrast to an Ornstein-Uhlenbeck process the restoring force is inversely proportional (or a power law with negative exponent) to the excursion distance from the sleep/wake border. We extend this model in [3] to account for the REM state and modify the restoring force law to account for deviations to the power law that are observed in data from some (but not all) labs and obtain a better fit to data [3].
[1] C.-C. Lo, L. A. Nunes Amaral, S. Havlin, P. Ch. Ivanov, T. Penzel, J.-H. Peter, and H. E. Stanley. Dynamics of sleep-wake transitions during sleep. Europhysics Letters, 57, 631, 2002.
[2] J. W. Kim, J. -S. Lee, P. A. Robinson, D. -U. Jeong, Markov Analysis of Sleep Dynamics. Phys. Rev. Lett. 102, 2009.
[3] A. Barkentien and J.C. Claussen (in preparation).