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Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction

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  • Lev Ryashko

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

  • Irina Bashkirtseva

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

Abstract

The Zeldovich–Semenov model of the continuous stirred tank reactor with parametric random disturbances in temperature is considered. We study a phenomenon of noise-induced transformation of the equilibrium mode into the mixed-mode oscillatory stochastic regime with alternations between small and large amplitudes. In the parametric analysis of the stochastic excitement, we use the analytical method of confidence domains based on the stochastic sensitivity technique. Analyzing a mutual arrangement of the confidence ellipses and separatrices, we estimate the critical intensity of the noise that causes the excitation. The phenomena of stochastic P-bifurcations and coherence resonances are discovered and studied by probability density functions and the statistics of interspike intervals.

Suggested Citation

  • Lev Ryashko & Irina Bashkirtseva, 2022. "Stochastic Bifurcations and Excitement in the ZS-Model of a Thermochemical Reaction," Mathematics, MDPI, vol. 10(6), pages 1-11, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:960-:d:773280
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    References listed on IDEAS

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    1. Jaimes-Reátegui, R. & García-López, J.H. & Gallegos, A. & Huerta Cuellar, G. & Chholak, P. & Pisarchik, A.N., 2021. "Deterministic coherence and anti-coherence resonances in networks of chaotic oscillators with frequency mismatch," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Xu, Chaoqun & Yuan, Sanling & Zhang, Tonghua, 2018. "Sensitivity analysis and feedback control of noise-induced extinction for competition chemostat model with mutualism," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 891-902.
    3. Lev Ryashko & Dmitri V. Alexandrov & Irina Bashkirtseva, 2021. "Analysis of Stochastic Generation and Shifts of Phantom Attractors in a Climate–Vegetation Dynamical Model," Mathematics, MDPI, vol. 9(12), pages 1-11, June.
    4. Sun, Yahui & Hong, Ling & Jiang, Jun, 2017. "Stochastic sensitivity analysis of nonautonomous nonlinear systems subjected to Poisson white noise," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 508-515.
    5. Simone Orcioni & Alessandra Paffi & Francesca Apollonio & Micaela Liberti, 2020. "Revealing Spectrum Features of Stochastic Neuron Spike Trains," Mathematics, MDPI, vol. 8(6), pages 1-13, June.
    6. Vjacheslav Danylenko & Sergiy Skurativskyi, 2014. "Stationary and periodic regimes in relaxing media with fluctuations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(9), pages 1-7, September.
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