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Canards Oscillations, Noise-Induced Splitting of Cycles and Transition to Chaos in Thermochemical Kinetics

Author

Listed:
  • Irina Bashkirtseva

    (Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia)

  • Grigoriy Ivanenko

    (Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia)

  • Dmitrii Mordovskikh

    (Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia)

  • Lev Ryashko

    (Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, Russia)

Abstract

We study how noise generates complex oscillatory regimes in the nonlinear thermochemical kinetics. In this study, the basic mathematical Zeldovich–Semenov model is used as a deterministic skeleton. We investigate the stochastic version of this model that takes into account multiplicative random fluctuations of temperature. In our study, we use direct numerical simulation of stochastic solutions with the subsequent statistical analysis of probability densities and Lyapunov exponents. In the parametric zone of Canard cycles, qualitative effects caused by random noise are identified and investigated. Stochastic P -bifurcations corresponding to noise-induced splitting of Canard oscillations are parametrically described. It is shown that such P -bifurcations are associated with splitting of both amplitudes and frequencies. Studying stochastic D -bifurcations, we localized the rather narrow parameter zone where transitions from order to chaos occur.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:8:p:1918-:d:1126870
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    References listed on IDEAS

    as
    1. 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).
    2. Richard B. Sowers, 2008. "Random Perturbations of Canards," Journal of Theoretical Probability, Springer, vol. 21(4), pages 824-889, December.
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