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Stochastic mixed-mode oscillations in the canards region of a cardiac action potential model

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  • Slepukhina, Evdokiia
  • Bashkirtseva, Irina
  • Ryashko, Lev
  • Kügler, Philipp

Abstract

Mixed-mode oscillations (MMOs) and canards play important role in the dynamics of many mathematical models in the life sciences. In particular, pathological early afterdepolarizations in heart cells behavior can be associated with MMOs. The present paper aims to study a stochastic version of the reduced Luo–Rudy model of cardiac action potential. We show that in the parameter zone where the dynamics of the original deterministic system is characterized by canard-type limit cycles, weak additive noise can induce MMOs. Using stochastic sensitivity functions, Mahalanobis metrics, and confidence domains, we analyze the probabilistic mechanism of this stochastic phenomenon. Moreover, we find a critical value of the parameter corresponding to the “super-sensitive” cycle and show that for this value, stochastic splitting of oscillations is observed. Furthermore, we show that in the canard zone of the model, noise-driven transition to chaos occurs. To conclude, this paper reveals and analyzes new stochastic phenomena in the model of cardiac activity, moreover, the presented results can be helpful for studies of other complex models.

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  • 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).
    • Handle: RePEc:eee:chsofr:v:164:y:2022:i:c:s0960077922008190
    DOI: 10.1016/j.chaos.2022.112640
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    References listed on IDEAS

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    1. Slepukhina, Evdokia & Bashkirtseva, Irina & Ryashko, Lev, 2020. "Stochastic spiking-bursting transitions in a neural birhythmic 3D model with the Lukyanov-Shilnikov bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
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    4. Irina Bashkirtseva & Lev Ryashko, 2017. "Stochastic sensitivity and variability of glycolytic oscillations in the randomly forced Sel’kov model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(1), pages 1-10, January.
    5. 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).
    6. Bashkirtseva, I.A. & Ryashko, L.B., 2004. "Stochastic sensitivity of 3D-cycles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 66(1), pages 55-67.
    7. 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.
    8. An, Xinlei & Qiao, Shuai, 2021. "The hidden, period-adding, mixed-mode oscillations and control in a HR neuron under electromagnetic induction," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
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    Cited by:

    1. Zhan, Feibiao & Su, Jianzhong & Liu, Shenquan, 2023. "Canards dynamics to explore the rhythm transition under electromagnetic induction," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    2. Irina Bashkirtseva & Grigoriy Ivanenko & Dmitrii Mordovskikh & Lev Ryashko, 2023. "Canards Oscillations, Noise-Induced Splitting of Cycles and Transition to Chaos in Thermochemical Kinetics," Mathematics, MDPI, vol. 11(8), pages 1-9, April.

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