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Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger

Author

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  • Irina Bashkirtseva

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

  • Makar Pavletsov

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

  • Tatyana Perevalova

    (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

Motivated by the increasingly important role of mathematical modeling and computer-aided analysis in engineering applications, we consider the problem of the mathematical modeling and computer-aided analysis of complex stochastic processes in thermo-kinetics. We study a mathematical model of the dynamic interaction of reagent concentration and temperature in autocatalysis. For the deterministic variant of this model, mono- and bistability parameter zones as well as local and global bifurcations are revealed, and we show how random multiplicative disturbances can deform coexisting equilibrium regimes. In a study of noise-induced transitions, we apply direct numerical simulation and an analytical approach based on the stochastic sensitivity technique. Two variants of bistability with different scenarios of stochastic transformations are studied and compared.

Suggested Citation

  • Irina Bashkirtseva & Makar Pavletsov & Tatyana Perevalova & Lev Ryashko, 2023. "Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger," Mathematics, MDPI, vol. 11(20), pages 1-14, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4302-:d:1260533
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    References listed on IDEAS

    as
    1. Bashkirtseva, Irina & Chukhareva, Anna & Ryashko, Lev, 2023. "Stochastic dynamics of nonlinear tumor–immune system with chemotherapy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    2. 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.
    3. Bashkirtseva, Irina & Ryashko, Lev, 2005. "Sensitivity and chaos control for the forced nonlinear oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1437-1451.
    4. 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.
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