Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger
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 dyn...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/11/20/4302 |
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| author | Irina Bashkirtseva Makar Pavletsov Tatyana Perevalova Lev Ryashko |
| author_facet | Irina Bashkirtseva Makar Pavletsov Tatyana Perevalova Lev Ryashko |
| author_sort | Irina Bashkirtseva |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T21:04:53Z |
| format | Article |
| id | doaj.art-9d08cd345e8f4fdaa7877627e247452d |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T21:04:53Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-9d08cd345e8f4fdaa7877627e247452d2023-11-19T17:14:05ZengMDPI AGMathematics2227-73902023-10-011120430210.3390/math11204302Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic TriggerIrina Bashkirtseva0Makar Pavletsov1Tatyana Perevalova2Lev Ryashko3Institute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, RussiaInstitute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, RussiaInstitute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, RussiaInstitute of Natural Sciences and Mathematics, Ural Federal University, Lenina 51, 620000 Ekaterinburg, RussiaMotivated 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.https://www.mdpi.com/2227-7390/11/20/4302noise-induced transitionsstochastic sensitivitythermo-kinetic modelautocatalytic trigger |
| spellingShingle | Irina Bashkirtseva Makar Pavletsov Tatyana Perevalova Lev Ryashko Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger Mathematics noise-induced transitions stochastic sensitivity thermo-kinetic model autocatalytic trigger |
| title | Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger |
| title_full | Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger |
| title_fullStr | Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger |
| title_full_unstemmed | Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger |
| title_short | Analysis of Noise-Induced Transitions in a Thermo-Kinetic Model of the Autocatalytic Trigger |
| title_sort | analysis of noise induced transitions in a thermo kinetic model of the autocatalytic trigger |
| topic | noise-induced transitions stochastic sensitivity thermo-kinetic model autocatalytic trigger |
| url | https://www.mdpi.com/2227-7390/11/20/4302 |
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