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Noise-induced early afterdepolarizations in a three-dimensional cardiac action potential model

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  • Slepukhina, E.
  • Ryashko, L.
  • Kügler, P.

Abstract

We study the influence of noise on a mathematical model of the cardiac action potential described by a three-dimensional system of ordinary differential equations. The original deterministic system undergoes a cascade of period adding saddle-node bifurcations resulting in the appearance of small scale oscillations that correspond to early afterdepolarizations (EADs). We consider a parameter region where the deterministic system exhibits normal action potential behavior and show that a small additive noise in gating variable dynamics can induce EADs in this region. This stochastic phenomenon is confirmed by changes in the probability density distributions for phase trajectories and inter-event intervals. These qualitative changes in the system dynamics can be considered as a special stochastic P-bifurcation. The mechanism of noise-induced EADs is studied with a new semi-analytical approach based on the stochastic sensitivity function technique, the method of confidence domains and Mahalanobis metrics. Applying this approach, we give an explanation of the probabilistic mechanism of the observed stochastic phenomenon and provide the estimations of critical noise intensities for the onset of noise-induced EADs.

Suggested Citation

  • Slepukhina, E. & Ryashko, L. & Kügler, P., 2020. "Noise-induced early afterdepolarizations in a three-dimensional cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    • Handle: RePEc:eee:chsofr:v:131:y:2020:i:c:s0960077919304679
    DOI: 10.1016/j.chaos.2019.109515
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    References listed on IDEAS

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    1. Liu, Meng & Wang, Ke, 2012. "Persistence and extinction of a single-species population system in a polluted environment with random perturbations and impulsive toxicant input," Chaos, Solitons & Fractals, Elsevier, vol. 45(12), pages 1541-1550.
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    5. Ryashko, L. & Bashkirtseva, I. & Gubkin, A. & Stikhin, P., 2009. "Confidence tori in the analysis of stochastic 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 256-269.
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    Cited by:

    1. Bashkirtseva, Irina & Kolinichenko, Alexander & Ryashko, Lev, 2021. "Stochastic sensitivity of Turing patterns: methods and applications to the analysis of noise-induced transitions," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    2. Jungeilges, Jochen & Pavletsov, Makar & Perevalova, Tatyana, 2022. "Noise-induced behavioral change driven by transient chaos," Chaos, Solitons & Fractals, Elsevier, vol. 158(C).
    3. Slepukhina, Evdokiia & Bashkirtseva, Irina & Ryashko, Lev & Kügler, Philipp, 2022. "Stochastic mixed-mode oscillations in the canards region of a cardiac action potential model," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).

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