Heart rate variability as determinism with  jump stochastic parameters

Jiongxuan Zheng; Joseph D. Skufca; Erik M. Bollt

doi:10.3934/mbe.2013.10.1253

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2013, Volume 10, Issue 4: 1253-1264. Doi: 10.3934/mbe.2013.10.1253

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Heart rate variability as determinism with jump stochastic parameters

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Received: April 30, 2012

Revised: December 31, 2012

Published: May 2013

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Abstract

We use measured heart rate information (RR intervals) to develop a one-dimensional nonlinear map that describes short term deterministic behavior in the data. Our study suggests that there is a stochastic parameter with persistence which causes the heart rate and rhythm system to wander about a bifurcation point. We propose a modified circle map with a jump process noise term as a model which can qualitatively capture such this behavior of low dimensional transient determinism with occasional (stochastically defined) jumps from one deterministic system to another within a one parameter family of deterministic systems.

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Mathematics Subject Classification: Primary: 15A15, 15A09, 15A23.

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