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Mathematical Biosciences and Engineering

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

  • 1.
    8 Clarkson AVE. P.O.5817, Potsdam, NY 13676
  • Received: 01 May 2012 Accepted: 29 June 2018 Published: 01 June 2013

  • MSC : Primary: 15A15, 15A09, 15A23.

  • 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.

    Citation: Jiongxuan Zheng, Joseph D. Skufca, Erik M. Bollt. Heart rate variability as determinism with jump stochastic parameters[J]. Mathematical Biosciences and Engineering, 2013, 10(4): 1253-1264. doi: 10.3934/mbe.2013.10.1253

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  • 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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  • © 2013 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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